Compute f '(a) algebraically for the given value of a. HINT [See Example 1.]
f(x) = −2x + 2; a = −5
f '(a) = 1Your answer is incorrect.
To compute f '(a) algebraically, we need to find the derivative of the function f(x) and then substitute the value of a into the derivative.
Given that f(x) = -2x + 2, we can find the derivative using the power rule for differentiation. The power rule states that if we have a function f(x) = ax^n, its derivative is f '(x) = n * ax^(n-1).
Applying the power rule, the derivative of f(x) = -2x + 2 is:
f '(x) = -2 * 1x^(1-1) = -2
Now, substitute the value of a = -5 into f '(x):
f '(-5) = -2
Therefore, the value of f '(a) for a = -5 is -2.