Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

If $f(x)=(1+x)^{5}=a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}+a_{4} x^{4}+a_{5} x^{5},$ use thepreceding exercise to find the values for the $a_{k}$ 's.

$$a_{0}=1, a_{1}=5, a_{2}=10, a_{3}=10, a_{4}=5, a_{5}=1$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 3

Concavity and the Second Derivative

Derivatives

Campbell University

Oregon State University

Baylor University

University of Nottingham

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

03:57

Express $f(x)$ in the form…

03:28

01:37

Write the function in the …

01:53

If $f(x)=a_{5} x^{5}+a_{4}…

00:57

$$\text { Find } f^{\prime…

the following problem, we're gonna want to use this previous results and we have the f of X equals one plus X to the fifth. Um And we want to find the values for the A. K. S. So knowing we have f of X equals One class except 5th. Okay. Mhm. Yeah, what we end up seeing is that we have um the night Is going to end up giving us just a zero, which is going to be one of the fifth, which is one, so 89 is equal to one. And if we take the first derivative, That's going to be a five, we plug in a zero, so it's five times one to the fourth. So to me five and then we're going to keep doing this, but now it's for um since we have a five in front and one of the one plus X to the fourth, we do it again and we'll end up getting 20 So a two will be 20 and this will keep going on and on.

View More Answers From This Book

Find Another Textbook

03:24

How much should be deposited into an account today if it is to accumulate to…

04:36

$$5 s^{2}\left(v^{3}-1\right)=7 . \text { Find }(a) d s / d v;(b) d v / d s$…

01:23

Use your calculator to compute the expression given.$$(-3.78)^{13}$$

01:48

If $f(x)=\sqrt{2 x-1},$ find $(a) f^{-1}(1)$,(b) $f^{-1}(3)$

01:15

Combine the given expression into a single logarithm.$$3 \ln x+2 \ln y$$…

00:55

Use your calculator to compute the expression given.$$4.7^{-3.21}$$

01:11

Determine if the given graph represents a one-to-one function.

02:58

Sketch the graph of the function defined by the given equation.$$f(x)=3^…

01:46

Determine the equation of the inverse function.$$f(x)=\sqrt{2 x+3}$$

01:10

Determine whether or not the function determined by the given equation is on…