Question

Suppose that f is a function given as f(x) = - 3x^2 - 4x + 2. Simplify the expression f(x + h). f(x + h) = Simplify the difference quotient, (f(x + h) - f(x)) / h. (f(x + h) - f(x)) / h = The derivative of the function at x is the limit of the difference quotient as h approaches zero. f'(x) = lim h->0 (f(x + h) - f(x)) / h = 

          Suppose that f is a function given as f(x) = - 3x^2 - 4x + 2.
Simplify the expression f(x + h).
f(x + h) =
Simplify the difference quotient, (f(x + h) - f(x)) / h.
(f(x + h) - f(x)) / h =
The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f'(x) = lim h->0 (f(x + h) - f(x)) / h =
Show more…
Suppose that f is a function given as f(x) = - 3x^2 - 4x + 2. Simplify the expression f(x + h). f(x + h) = Simplify the difference quotient, (f(x + h) - f(x)) / h. (f(x + h) - f(x)) / h = The derivative of the function at x is the limit of the difference quotient as h approaches zero. f'(x) = lim h->0 (f(x + h) - f(x)) / h =

Added by Jodi S.

Close

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Suppose that f is a function given as f(x) = - 3x^2 - 4x + 2. Simplify the expression f(x + h). f(x + h) = Simplify the difference quotient, (f(x + h) - f(x)) / h. (f(x + h) - f(x)) / h = The derivative of the function at x is the limit of the difference quotient as h approaches zero. f'(x) = lim h->0 (f(x + h) - f(x)) / h =
Close icon
Play audio
Feedback
Powered by NumerAI
David Collins Kathleen Carty
Danielle Fairburn verified

Zhumagali Shomanov and 51 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.
*

Recommended Videos

-
suppose-that-f-is-a-function-given-as-fx-follows-7-we-will-compute-the-derivative-of-f-at-r-2-as-first-we-will-compute-and-simplify-the-expression-f2-h-f2-h-then-we-compute-and-simplify-the-85163

Suppose that f is a function given as f(x) = -6x + 7. We will compute the derivative of f at x = 2 as follows. First, we will compute and simplify the expression f(2 + h). f(2 + h) = Then we compute and simplify the difference quotient between x = 2 and x = 2 + h. (f(2 + h) - f(2)) / h = The derivative of the function at x = 2 is the limit of the difference quotient as h approaches zero. f'(2) = lim_{h->0} (f(2 + h) - f(2)) / h =

Khushbu R.
fx-h-fx-find-and-simplify-the-difference-quotient-h0-for-the-given-function-fx-3x-tx-h-fx-simplify-your-answer-now-find-take-the-limit-fx-h-fx-lim-h-0-simplify-your-answer-97393

Find and simplify the difference quotient f(x + h) - f(x) / h, h ≠ 0 for the given function: f(x) = 3x^2 f(x + h) - f(x) / h = (Simplify your answer.) Now, Find take the limit lim h->0 f(x + h) - f(x) / h = (Simplify your answer.)

Steven C.
differentiate-the-function-by-forming-the-difference-quotient-fracfxh-fxh-and-taking-the-limit-as--8

Differentiate the function by forming the difference quotient $$\frac{f(x+h)-f(x)}{h}$$ and taking the limit as $h$ tends to $0 .$ $$f(x)=x^{3}-4 x$$

Calculus: One Variable

The Derivative; The Process of Differentiation

The Derivative
*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,988 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,303 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,955 solutions
*

Transcript

-
00:01 In this question, we are asked to calculate the derivative of the function f using the definition of the derivative.
00:07 And first we need to calculate f of x plus h.
00:11 And to do that, we need to plug in x plus h for x in the formula for f, and we are going to get negative 3 times x plus h squared minus 4 times x plus h plus 2.
00:28 Now let's expand that expression.
00:30 We are going to get negative 3 times x squared plus 2 x h plus h squared minus 4 x minus 4 h plus 2 and this further simplifies to negative 3 x squared minus 6 x h minus 3h squared minus 4 x x minus 4 h plus 2 now we need to calculate the difference quotient f of x plus h minus f of x over h.
01:12 So what we are going to do is we will rewrite the expression we found in the previous step for f of x plus h.
01:30 And subtract f of x from that.
01:33 Recall that f of x is negative 3x squared minus 4x plus 2 divided by h.
01:47 Next we can cancel negative 3x squared, we can cancel negative 4x and we can cancel 2...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade

Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever