Final answer:
To find the derivative of the function f(x) = 7 + x^2, we differentiate each term separately and add them up using the power rule. The values of the derivative at specific points are f'(-9) = -18, f'(0) = 0, and f'(5) = 10.
Step-by-step explanation:
To find the derivative of a function using the power rule, we differentiate each term separately and then add them up. For the given function f(x) = 7 + x^2, we have:
f'(x) = 0 + 2x = 2x
To find the values of the derivative at specific points, we substitute the given x-values into the derivative and evaluate:
f'(-9) = 2(-9) = -18
f'(0) = 2(0) = 0
f'(5) = 2(5) = 10