If f(x) = x^2 + 2x + 1, what is f'(1)?

If f(x) = x^2 + 2x + 1, what is f'(1)?

Step 1: Identify the function f(x) = x^2 + 2x + 1.
Step 2: Find the derivative of the function f(x). The derivative f'(x) tells us the rate of change of f(x).
Step 3: Use the power rule to differentiate each term: The derivative of x^2 is 2x, the derivative of 2x is 2, and the derivative of 1 is 0.
Step 4: Combine the derivatives to get f'(x) = 2x + 2.
Step 5: Now, we need to find f'(1). Substitute x = 1 into the derivative: f'(1) = 2(1) + 2.
Step 6: Calculate f'(1): 2(1) + 2 = 2 + 2 = 4.

Derivative Calculation – The question tests the ability to find the derivative of a polynomial function and evaluate it at a specific point.
Function Evaluation – It assesses the understanding of substituting a value into a derived function.