Question

If f(x)=(2x−1)⁴, then the 4th derivative of f(x) at x=0 is:

A. 0
B. 2^(4) .⋅4!
C. 4!
D. 24

Answer 1

The 4th derivative of f(x) = (2x - 1)⁴ at x = 0 is 0.

Step-by-step explanation:

The question asks for the 4th derivative of the function f(x) = (2x - 1)⁴ at x = 0. To find the 4th derivative, we need to differentiate the function 4 times. Here are the steps:

Step 1: Find the 1st derivative of f(x): f'(x) = 4(2x - 1)³

Step 2: Find the 2nd derivative of f(x): f''(x) = 12(2x - 1)²

Step 3: Find the 3rd derivative of f(x): f'''(x) = 24(2x - 1)

Step 4: Find the 4th derivative of f(x): f''''(x) = 24

Now, substitute x = 0 into the 4th derivative to find the value at x = 0. Since the derivative of a constant is always 0, the 4th derivative of f(x) at x = 0 is A. 0.