Consider the function. Find f'(x). f'(x) = Find F"(x). f"(x) = f(x) = x³6x² +9 Find f"(-3) and f"(9). f"(-3) = f"(9) = Determine whether the function f(x) is concave up or concave down at the indicated points. (a) x = -3 (b) x = 9 concave up concave down concave up concave down

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the function.

\( f(x) = x^3 - 6x^2 + 9 \)

**Find \( f'(x) \).**

\( f'(x) = \) [Textbox]

**Find \( f''(x) \).**

\( f''(x) = \) [Textbox]

**Find \( f''(-3) \) and \( f''(9) \).**

\( f''(-3) = \) [Textbox]  
\( f''(9) = \) [Textbox]

**Determine whether the function \( f(x) \) is concave up or concave down at the indicated points.**

(a) \( x = -3 \)  
- [ ] concave up  
- [ ] concave down  

(b) \( x = 9 \)  
- [ ] concave up  
- [ ] concave down
Transcribed Image Text:Consider the function. \( f(x) = x^3 - 6x^2 + 9 \) **Find \( f'(x) \).** \( f'(x) = \) [Textbox] **Find \( f''(x) \).** \( f''(x) = \) [Textbox] **Find \( f''(-3) \) and \( f''(9) \).** \( f''(-3) = \) [Textbox] \( f''(9) = \) [Textbox] **Determine whether the function \( f(x) \) is concave up or concave down at the indicated points.** (a) \( x = -3 \) - [ ] concave up - [ ] concave down (b) \( x = 9 \) - [ ] concave up - [ ] concave down
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