"(x). "'(x). "(-9) and f"(7). = f(x) = x³ 3x² +7 mine whether the function f(x) is concave up or concave down at the indicated points. x = -9 x = 7 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.

\[ f(x) = x^3 - 3x^2 + 7 \]

Find \( f'(x) \).

\[ f'(x) = \]

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

\[ f''(x) = \]

Find \( f''(-9) \) and \( f''(7) \).

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

\[ f''(7) = \]

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

(a) \( x = -9 \)
- ○ concave up
- ○ concave down

(b) \( x = 7 \)
- ○ concave up
- ○ concave down
Transcribed Image Text:Consider the function. \[ f(x) = x^3 - 3x^2 + 7 \] Find \( f'(x) \). \[ f'(x) = \] Find \( f''(x) \). \[ f''(x) = \] Find \( f''(-9) \) and \( f''(7) \). \[ f''(-9) = \] \[ f''(7) = \] Determine whether the function \( f(x) \) is concave up or concave down at the indicated points. (a) \( x = -9 \) - ○ concave up - ○ concave down (b) \( x = 7 \) - ○ concave up - ○ concave down
Expert Solution
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Topic:- derivatives and application of derivatives  

 

Definition:-

When the second derivative is positive, the function is concave upward. When the second derivative is negative, the function is concave downward.

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