Question

Compute f'(a) algebraically for f(x) = -9x - x^2; a = 9:

a) 27
b) -18
c) 18
d) -27

Answer 1

The value of function f'(a) for f(x) = -9x - x^2, when a = 9 is calcuated to be as f'(a) = -27. Option D is answer.

Step-by-step explanation:

To find f'(a), we first need to find the derivative of f(x). The derivative of -9x - x^2 is -9 - 2x.

Therefore, f'(x) = -9 - 2x.

Now, we can plug in a = 9 to find f'(a):

f'(a) = -9 - 2 * 9

f'(a) = -9 - 18

f'(a) = -27

Therefore, the answer is d) -27.

In conclusion, the value of the derivative function f'(a) for f(x) = -9x - x^2, when evaluated at a = 9, is calculated to be -27. This result is derived from finding the derivative of the given function and substituting the specific value of a. Option D accurately represents this outcome as the answer.