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f"(x) = f(x) = (x + 6)(x − 6)(x +,5)(x – 5) X Solve the equation f'(x) = 0. (Enter your answers as a co

f"(x) = f(x) = (x + 6)(x − 6)(x +,5)(x – 5) X Solve the equation f'(x) = 0. (Enter your answers as a co

Calculus: Early Transcendentals
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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We need to Find the second derivative and solve the equation
### Problem Overview Given the function: \[ f(x) = (x + 6)(x - 6)(x + 0.5)(x - 5) \] ### Task 1. Find the third derivative of the function, \( f'''(x) \). 2. Solve the equation \( f'''(x) = 0 \). ### Steps to Solve #### 1. Finding \( f'''(x) \) - First, expand the given polynomial. - Differentiate the expanded polynomial three times to find \( f'''(x) \). #### 2. Solving \( f'''(x) = 0 \) - Set the third derivative equal to zero. - Solve for the values of \( x \). ### Incorrect Solutions The answer box displays: \[ x = -\sqrt{\boxed{\phantom{5}}}, \sqrt{\boxed{\phantom{5}}} \] ### Note - Ensure your calculations for the third derivative and solving \( f'''(x) = 0 \) are accurate. - Double-check the provided answers for any placeholders or inaccuracies.
Transcribed Image Text:### Problem Overview Given the function: \[ f(x) = (x + 6)(x - 6)(x + 0.5)(x - 5) \] ### Task 1. Find the third derivative of the function, \( f'''(x) \). 2. Solve the equation \( f'''(x) = 0 \). ### Steps to Solve #### 1. Finding \( f'''(x) \) - First, expand the given polynomial. - Differentiate the expanded polynomial three times to find \( f'''(x) \). #### 2. Solving \( f'''(x) = 0 \) - Set the third derivative equal to zero. - Solve for the values of \( x \). ### Incorrect Solutions The answer box displays: \[ x = -\sqrt{\boxed{\phantom{5}}}, \sqrt{\boxed{\phantom{5}}} \] ### Note - Ensure your calculations for the third derivative and solving \( f'''(x) = 0 \) are accurate. - Double-check the provided answers for any placeholders or inaccuracies.
Expert Solution
Step 1: to find

To find second derivative of

f left parenthesis x right parenthesis equals open parentheses x plus 6 close parentheses open parentheses x minus 6 close parentheses open parentheses x plus 5 close parentheses open parentheses x minus 5 close parentheses

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