Problem

(a) Graph the function $ g(x) = e^x - 3x^2 $ in t…

02:08

Problem 43 Medium Difficulty

(a) Graph the function
$ f(x) = x^4 - 3x^3 - 6x^2 + 7x + 30 $
in the viewing rectangle [-3,5] by [-10,50].
(b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of $ f' $.
(c) Calculate $ f'(x) $ and use this expression, with graphing device, to graph $ f' $. Compare with your sketch in part (b).

Answer

(a)
(b) Positive (so $f^{\prime}$ is positive) on $\left(x_{1}, x_{2}\right)$ and $\left(x_{3}, \infty\right)$
(c) $$f^{\prime}(x)=4 x^{3}-9 x^{2}-12 x+7$$

More Answers

00:29

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

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Video Transcript

Hey, it's close when you read here. So for part A, I'll draw our graph, and it looks something like this for part B. We have All right, um, graph of our original and then we're gonna graph are derivative. I'll do it in green. So you have. And then you finally, for part C, we're going to find our We're gonna difference she our original function and we get this is equal to for X cubed minus nine X square minus 12 x my seven. And when we grab this, I look like this.

Clarissa N.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University