Question

Compute f '(a) algebraically for the given value of a.
f(x) = x² − 9; a = 1

Answer 1

To compute f'(a) for f(x) = x² − 9 at a = 1, find the derivative f'(x) = 2x. Then substitute a = 1 into the derivative to get f'(1) = 2.

Step-by-step explanation:

To compute f'(a) algebraically for the given function f(x) = x² − 9 when a = 1, we must first find the derivative of f(x) with respect to x. The derivative of x² is 2x, and the derivative of a constant like −9 is 0. Thus, f'(x) = 2x.

Next, we substitute a = 1 into the derivative to find f'(a). So, f'(1) = 2(1) = 2. This gives us the slope of the tangent line to the graph of f(x) = x² − 9 at the point where x = 1.