Question

Compute f '(a) algebraically for the given value of a. HINT [See Example 1.]

f(x) = x2 − 9; a = 1

Answer 1

To compute f'(a) algebraically for the given value a = 1, we need to find the derivative of the function f(x) = x^2 - 9. The derivative of f(x) is 2x, so substituting a=1 gives f'(1) = 2.

Step-by-step explanation:

To compute f'(a) algebraically for the given value a = 1, we need to find the derivative of the function f(x) = x^2 - 9. The derivative of a function measures its rate of change at any given point on the graph. First, we find the derivative of each term using the power rule:

For the term x^2, the derivative is 2x. For the term -9, the derivative is 0 since it is a constant.

Combining these derivatives, we get f'(x) = 2x. Now, substitute the value a = 1 into the derivative to find f'(1).

Plugging in x = 1, we get f'(1) = 2(1) = 2.