Final answer:
To find the derivative of the function f(x) = (x² - 3)² at x = 1, we need to use the chain rule. The derivative is -8, so the correct answer is (D) 32.
Step-by-step explanation:
To find the derivative of the function f(x) = (x² - 3)² at x = 1, we need to use the chain rule. The chain rule states that if we have a composite function g(f(x)), then the derivative of g(f(x)) with respect to x is given by g'(f(x)) * f'(x).
First, let's find the derivative of the outer function g(x) = x² - 3, which is 2(x² - 3). Then, let's find the derivative of the inner function f(x) = x² - 3, which is 2x. Finally, we can substitute x = 1 into both derivatives and multiply them together to find f'(1).
g'(1) = 2(1² - 3) = -4
f'(1) = 2(1) = 2
f'(1) = g'(1) * f'(1) = -4 * 2 = -8
Therefore, the correct answer is (D) 32.