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

Find a cubic function $ y = ax^3 + bx^2 + cx + d $ whose graph has horizontal tangent at the points (-2, 6) and (2, 0).

$$y=\frac{3}{16} x^{3}-\frac{9}{4} x+3$$

03:57

Clarissa N.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

Idaho State University

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

07:01

Find a cubic function $y=a…

02:08

Determine an equation of t…

05:36

find an equation of the ta…

06:02

Find the points on the cur…

01:28

0:00

Find the point on the grap…

01:33

Find the parabola with equ…

01:15

Find an equation of the ta…

00:49

01:40

a. Find an equation of the…

he had slower. So when you right here. So we have. Why is equal to a X cute? Must be X square plus feet x plus D you differentiate this to get three a X Square plus two B X? Let's see. We're gonna set up our equations from our given points, so we have negative to calm a six when we plug it into the original equation. We got six in our line ISS negative. Eat a That's four p minus two C plus T is equal to six. Then we have 0.2 comma zero. When we plug it into our original equation, we good cereal. Yeah, a Ame plus four B plus two C plus D is equal to zero. Where are derivatives since there's horizontal tangents, the derivative for positive and negative, too, is equal to zero, so we go for negative to calm a six. You get our derivative to be equal to zero well, a minus four B plus C. It's equal to zero and for our point to calm a zero. This is also there as well, since there are horizontal tangents. 12 a plus four B plus C is equal to zero then we're going to subtract our equations. 12 day was for P. Thus he is equal to zero minus 12. A finest for P plus C is equal to zero. Then we got B is equal to zero. We're gonna add up our equations. Our 1st 2 equations less for B plus two c rusty this equal to zero. Then we got Dee as equal to three. Since we plug in, zero for B C is equal to negative 12 A. When we get a was four times zero plus two negative 12 a plus three is equal to zero. Can we get a value of three over 16? And when we plug it in, C becomes negative nine over four. Then we just plug it in to get wise people to three over 16 x square x cubed Excuse me minus nine over four x plus three

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…

Find a cubic function $y=a x^{3}+b x^{2}+c x+d$ whose graph has horizontal t…

Determine an equation of the line tangent to the graph of $y=\frac{\left(x^{…

find an equation of the tangent line at the given point.$$x y+x^{2} …

Find the points on the curve $y=2 x^{3}+3 x^{2}-12 x+1$ where the tangent is…

Find the point on the graph of $f(x)=x^{3}$ such that the tangent line at th…

Find the parabola with equation $ y = ax^2 + bx $ whose tangent line at (1, …

Find an equation of the tangent line to the curve at the given point.$ y…

Find the points on the curve $ y = 2x^3 + 3x^2 - 12x + 1 $ where the tangent…

a. Find an equation of the line tangent to the given curve at a.b. Use a…

00:52

Differentiate.

$ y = \frac {e^x}{1 - e^x} $

11:07

Find the derivative of the function using the definition of derivative. Stat…

04:00

Find the volume of the described solid $ S $.A frustum of a pyramid with…

00:33

Differentiate the function.$ z = \frac {A}{y^{10}} + Be^y $

00:22

Find the first and second derivatives of the function. Check to see that you…

00:29

$ f(x) = e^x $ cos $ x $

02:45

Refer to the figure and find the volume generated by rotating the given regi…

03:15

(a) How large do we have to take $ x $ so that $ 1/\sqrt{x} < 0.0001 $?<…

03:19

Find the horizontal and vertical asymptotes of each curve. If you have a gra…

02:15

Find $ f'(x) $ and $ f"(x). $

$ f(x) = \frac {x^2}{1 + e^x…

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.