Question: Determine the critical points of f(x) = x^4 - 8x^2 + 16.
Options:
x = 0, ±2
x = ±4
x = ±1
x = 2
Correct Answer: x = 0, ±2
Solution:
Setting f\'(x) = 0 gives critical points at x = 0, ±2.
Determine the critical points of f(x) = x^4 - 8x^2 + 16.
Practice Questions
Q1
Determine the critical points of f(x) = x^4 - 8x^2 + 16.
x = 0, ±2
x = ±4
x = ±1
x = 2
Questions & Step-by-Step Solutions
Determine the critical points of f(x) = x^4 - 8x^2 + 16.
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.
Finding Critical Points – This involves taking the derivative of the function and setting it to zero to find points where the function's slope is zero.
Polynomial Functions – Understanding the behavior of polynomial functions, including their derivatives and how to find maxima and minima.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
