Refer a friend and earn $50 when they subscribe to an annual planRefer Now
Get the answer to your homework problem.
Try Numerade Free for 30 Days
Like
Report
Minimum Distance, find the points on the graph of the function that are closest to the given point.
$y=x^{2}-2,(0,-1)$
(ANSWER NOT AVAILABLE)
Calculus 1 / AB
Chapter 3
Applications of Differentiation
Section 7
Optimization Problems
Limits
Derivatives
Differentiation
Oregon State University
Harvey Mudd College
University of Michigan - Ann Arbor
Idaho State University
Lectures
03:09
In mathematics, precalculu…
31:55
In mathematics, a function…
09:07
Minimum Distance, find the…
03:54
Minimum Distance Find the …
04:14
Find the minimum distance …
06:40
02:18
Find the point on the line…
00:34
04:26
Constrained minimum Find t…
03:27
01:46
Which point on the curve $…
04:20
What is the minimum vertic…
So you know it. We need to find a function where, Trevor, than the distance between point on a curve and the point they're coming to get one now. Any pointing a curve? Coordinate X comma. I squared my too. And now that we have 2.3 canopied a distant one month D did you or choir room back mining? You think this is our personal second point? The first coin. Excellent job square. What? And then square my two money negative one. Nothing squared. All right, I'm making simplify that to make and then you're going to be X squared. Uh, mining one squared. All right, You're the function of X. Um, I gotta square root. And to make this the competition a little bit here, you better make movies are function. We're going to make d squared are functions we escorted side of the equation. We'll get, uh, square X squared, minus one. Where and this we're going to make we're going to call it f of X now. So if we minimise at vexed, then for minimizing this B squared square, didn't But when the square of the beautiful minimize the This is awesome. In a mine. So that's okay. We can just minimize the simpler functions. And now we need upon the minimum the function. Uh, I'd like to find the derivative like you could for a derivative test to find the minimum before you do that, though might simplify the function. So expand out the term we get next group quiet. Except for my two X squared clash one. When combining terms, we get extra before my ex crim one. All right. And now we're ready to find a minimum of dysfunction. Take the derivative. We'll do the first relative test we need to find where the derivative equal to zero. So the derivative is the function for him. My direction and next, like, finally, it's derivative equal to zero so that it equals zero for executing on a direction. And then this offer actress factor. So, Nero, you go factor on eggs. But I wasn't even talking to exterior. We will get Greg my one and now get to the ball Inclusion to actually pull a girl or the following equation. Brother Practical. They're out and two X squared minus one equals zero. And here forget I equals zero. It's a critical point And here I saw for X and take the square root. So we'll get after my Gregory, Uh, 1/2 which could be rational. I, uh, like your mind, uh, squared of you over too. All right, here are 33 critical numbers in critical point and the fish to figure out which one of the minimum. That's quite a first derivative. Uh huh. We're going to set up a number line for the value of driven it when we have euro. You're an incredible number of your hero. Question. My reach over to that would put her. Told me to be here somewhere. Well, negativity will be too very somewhere, and we need to find out when the derivative positive and one negative. Uh, so you critical number. They're going to break break up our number one in the interval. And so to figure out the door of a positive or negative somewhere next point into the derivative. So I took the point on here. It could be any point. So much of you 10. Kind of. Definitely bigger. Require October tail. You're a fucking 10 into the derivative. Here. We'll get four time. Really? Our number, uh, 5000 minus 20. Definitely a positive number. Derivative is positive here. And then somebody will be here in, like, a fucking negative 10. So negative, uh, we'll get a really large negative number. Negative point outing that my next to time. Take your time. Pointed a negative number. All right. Next. You can try number in here so we could do, like, negative 0.1, for example. And if you the calculator negative 0.1, you'll find a derivative positive. You're and over here could plug in positive 0.1, and you'll find a derivative negative. All right, So the minimum of a function occurs when the derivative goes from positive to negative and look like this. Excuse me. Uh, negative. Positive affected. So visualize the minimum value. Look, I've drawn it wrong. Thanks, man. I'm saying the correct word, but I'm sure the wrong picture. So from negative to positive, I mean, their function decreasing angry thing like this off. It's negative, goes up, goes down and the negative positive come off. So so? And so we see that negative were to over two. One positive. It's over to These are both minimum value throwing ex Nichols what? Their money makeover too. The function minimize. Remember, this function represents it doesn't square. That means for these acts value. This is between the curve and the point of being minimized. Now, we're not done. We need to find the actual point on a curve. Well, we just started echoed by you. So I just plug back into this equation for the curb to find out why that you. So we dug in, um, re plugging routes over to function. Do you, like, with a record amount of two, and we'll get, uh, to over four. Oh, they did more than think I'm actually, uh, when we No matter, we need a positive or the negative. We're going to get a positive. The fourth minus two, which turned out to be negative three house. That's going to be this. Whether or not we're talking a positive printer, beauty or negative, it over to that number is being squared. All right, so let's give it a two point. They have negative. You over too. Promise. Negative rehab. Now the positive rich over too. Do we have need of a two point on the curve, like with great to my two, which are closest to the 0.0
View More Answers From This Book
Find Another Textbook
In mathematics, precalculus is the study of functions (as opposed to calculu…
In mathematics, a function (or map) f from a set X to a set Y is a rule whic…
Minimum Distance, find the points on the graph of the function that are clos…
Minimum Distance Find the point on the graph of the equation$$16 x=y^{2}…
Find the minimum distance from the parabola $y=x^{2}$ to point $(0,3)$
Minimum Distance Find the point on the graph of the function$$x=\sqrt{10…
Find the point on the line whose equation is 2x + y - 2 = 0 that is closest …
Find the point on the line $y=x$ that is closest to the point $(3,1) .$ [Hin…
Constrained minimum Find the points on the curve $x^{2} y=2$nearest the …
Constrained minimum Find the points on the curve $x^{2} y=2$ nearest the ori…
Which point on the curve $y=\sqrt{x-2}+1$ is closest to the point (4,1)$?$ W…
What is the minimum vertical distance between the parabolas $ y = x^2 + 1 $ …
03:17
In Exercises 17-36, find the limit, if it exists.$$\lim _{x \rightarrow…
02:08
Analyzing the Graph of a Function Exercises $9-36,$ analyze and sketch a gra…
06:16
Numerical, Graphical, and Analytic Analysis An exercise room consists of a r…
03:10
Writing In your own words, describe primary equation, secondary equation, an…
08:03
Points of Intersection In Exercises $17-20$ , apply Newton's Method to …
01:51
The efficiency (in percent) of an internal combustion engine is Efficien…
02:03
Using Rolle's Theorem In Exercises $7-10$ , find the two $x$ -intereept…
02:07
Using Trigonometric Functions(a) Find the derivative of the function $g(…
00:17
Writing a Definite Integral In Exercises $5 - 10$ , write a definite integra…
06:12
92% of Numerade students report better grades.
Try Numerade Free for 30 Days. You can cancel at any time.
Annual
0.00/mo 0.00/mo
Billed annually at 0.00/yr after free trial
Monthly
0.00/mo
Billed monthly at 0.00/mo after free trial
Earn better grades with our study tools:
Textbooks
Video lessons matched directly to the problems in your textbooks.
Ask a Question
Can't find a question? Ask our 30,000+ educators for help.
Courses
Watch full-length courses, covering key principles and concepts.
AI Tutor
Receive weekly guidance from the world’s first A.I. Tutor, Ace.
30 day free trial, then pay 0.00/month
30 day free trial, then pay 0.00/year
You can cancel anytime
OR PAY WITH
Your subscription has started!
The number 2 is also the smallest & first prime number (since every other even number is divisible by two).
If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".
Receive weekly guidance from the world's first A.I. Tutor, Ace.
Mount Everest weighs an estimated 357 trillion pounds
Snapshot a problem with the Numerade app, and we'll give you the video solution.
A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.
Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.