Question

4. Consider the function $f(x) = x^4 - 2x^3$. (a) Find the zeros of $f(x)$. (b) Compute $f'(x)$ and $f''(x)$. (c) Find all inflection points of $f(x)$. When is $f(x)$ concave up? When is it concave down? (d) Compute $\lim_{x \to \infty} f(x)$ and $\lim_{x \to -\infty} f(x)$. (e) Use your answers from the previous parts to provide a rough sketch of $f(x)$. (Do not use desmos.com or any other online calculator!) (f) Consider the function $g(x) = (x+10)^4 - 2(x+10)^3 - 17$. Without computing any derivatives, what are the inflection points of $g(x)$? How do you know?

          4. Consider the function $f(x) = x^4 - 2x^3$.
(a) Find the zeros of $f(x)$.
(b) Compute $f'(x)$ and $f''(x)$.
(c) Find all inflection points of $f(x)$. When is $f(x)$ concave up? When is it concave down?
(d) Compute $\lim_{x \to \infty} f(x)$ and $\lim_{x \to -\infty} f(x)$.
(e) Use your answers from the previous parts to provide a rough sketch of $f(x)$. (Do not use
desmos.com or any other online calculator!)
(f) Consider the function $g(x) = (x+10)^4 - 2(x+10)^3 - 17$. Without computing any derivatives,
what are the inflection points of $g(x)$? How do you know?

Show more…

4. Consider the function f(x) = x^4 - 2x^3.
(a) Find the zeros of f(x).
(b) Compute f'(x) and f”(x).
(c) Find all inflection points of f(x). When is f(x) concave up? When is it concave down?
(d) Compute limx →∞ f(x) and limx → -∞ f(x).
(e) Use your answers from the previous parts to provide a rough sketch of f(x). (Do not use
desmos.com or any other online calculator!)
(f) Consider the function g(x) = (x+10)^4 - 2(x+10)^3 - 17. Without computing any derivatives,
what are the inflection points of g(x)? How do you know?

Added by Chelsea Z.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

10/08/2023

Step 1

To find the zeros of f(x), we set f(x) = 0 and solve for x: x^4 - 2x^3 = 0 x^3(x - 2) = 0 This gives us x = 0 and x = 2 as the zeros of f(x). Show more…

Show all steps

lock

Thanks for your feedback!

Consider the function f(x) = x^4 - 2x^3. (a) Find the zeros of f(x). (b) Compute f'(x) and f''(x). (c) Find all inflection points of f(x). When is f(x) concave up? When is it concave down? (d) Compute lim_(x->∞) f(x) and lim_(x->-∞) f(x). (e) Use your answers from the previous parts to provide a rough sketch of f(x). (Do not use desmos.com or any other online calculator!) (f) Consider the function g(x) = (x + 10)^4 - 2(x + 10)^3 - 17. Without computing any derivatives, what are the inflection points of g(x)? How do you know? 4. Consider the function f = x^4 - 2. (a) Find the zeros of f. (b) Compute f' and f''. (c) Find all inflection points of f. When is f concave up? When is it concave down? (d) Compute lim f and lim f. (e) Use your answers from the previous parts to provide a rough sketch of f. (Do not use desmos.com or any other online calculator!) (f) Consider the function g(x) = (x + 10)^4 - 2(x + 10)^3 - 17. Without computing any derivatives, what are the inflection points of g? How do you know?

Play audio

Feedback

Powered by NumerAI

Adi S and 88 other subject Physics 103 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

Recommended Videos

Recommended Textbooks

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

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