Compute f '(a) algebraically for the given value of a. HINT [See Example 1.]
f(x) = −2x + 2; a = −5
To compute f '(a) algebraically, we need to find the derivative of the function f(x) = −2x + 2 and then substitute the given value of a, which is −5. Let's go through the steps.
Step 1: Find the derivative of f(x)
The derivative of a linear function is simply the coefficient of x. In this case, f(x) = −2x + 2, so the derivative of f(x) with respect to x is:
f '(x) = -2
Step 2: Substitute the given value of a
To find f '(a), we substitute x with a in the derivative equation:
f '(a) = -2
So the derivative of f(x) = −2x + 2 with respect to x, evaluated at a = −5, is equal to -2.
Proofread your question before you post it. I assume a = x.
f(-5) = 10 + 2 = ?