Problem

The equation of motion of a particle is $ = t^3 -…

01:59

Problem 48 Medium Difficulty

Find the first and second derivatives of the function. Check to see that your answers are reasonable by comparing the graphs of $ f, f', $ and $ f". $
$ f(x) = e^x - x^3 $

Answer

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Discussion

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Video Transcript

Hey, it's clear. So when you read here is so we have f of X is equal to I need to the ex minus X cubed We could differentiate when we get beat to the ex minus three X square And to get our second derivative, we just differentiate first we gotta eat the X minus six x We're gonna draw our graph up with them all together at once. So original function enough of X while doing black and I'll look like this are derivative is in red and our second derivative is in green.

Clarissa N.

Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Top Calculus 1 / AB Educators

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Oregon State University

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Problem

The equation of motion of a particle is $ = t^3 -…

Problem 48 Medium Difficulty

Find the first and second derivatives of the function. Check to see that your answers are reasonable by comparing the graphs of $ f, f', $ and $ f". $
$ f(x) = e^x - x^3 $

Answer

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 1 / AB Educators

Grace H.

Catherine R.

Heather Z.

Samuel H.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

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Watch More Solved Questions in Chapter 3

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Kristen K.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

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Problem

The equation of motion of a particle is $ = t^3 -…

Problem 48 Medium Difficulty

Find the first and second derivatives of the function. Check to see that your answers are reasonable by comparing the graphs of $ f, f', $ and $ f". $$ f(x) = e^x - x^3 $

Answer

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 1 / AB Educators

Grace H.

Catherine R.

Heather Z.

Samuel H.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Kristen K.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Find the first and second derivatives of the function. Check to see that your answers are reasonable by comparing the graphs of $ f, f', $ and $ f". $
$ f(x) = e^x - x^3 $