21–30. Derivatives
b. Evaluate f'(a) for the given values of a.
f(s) = 4s³+3s; a= -3, -1

Verified step by step guidance

1. Step 1: Identify the function f(s) = 4s^3 + 3s and the values of a for which we need to evaluate the derivative, which are a = -3 and a = -1.
2. Step 2: Find the derivative of the function f(s) with respect to s. Use the power rule, which states that the derivative of s^n is n*s^(n-1).
3. Step 3: Apply the power rule to each term in the function. The derivative of 4s^3 is 12s^2, and the derivative of 3s is 3.
4. Step 4: Combine the derivatives to get the derivative function f'(s) = 12s^2 + 3.
5. Step 5: Evaluate the derivative at the given values of a. Substitute s = -3 into f'(s) to find f'(-3), and substitute s = -1 into f'(s) to find f'(-1).