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Determine the critical points of f(x) = x^4 - 8x^2 + 16.
Determine the critical points of f(x) = x^4 - 8x^2 + 16.
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Practice Questions
1 question
Q1
Determine the critical points of f(x) = x^4 - 8x^2 + 16.
x = 0, ±2
x = ±4
x = ±1
x = 2
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Setting f'(x) = 0 gives critical points at x = 0, ±2.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the critical points of f(x) = x^4 - 8x^2 + 16.
Solution:
Setting f'(x) = 0 gives critical points at x = 0, ±2.
Steps: 5
Show Steps
Step 1: Write down the function f(x) = x^4 - 8x^2 + 16.
Step 2: Find the derivative of the function, f'(x).
Step 3: Set the derivative f'(x) equal to 0 to find critical points.
Step 4: Solve the equation f'(x) = 0 for x.
Step 5: Identify the values of x that you found in Step 4 as the critical points.
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