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). This means we will substitute x = 1 into the derivative f'(x).
Step 6: Substitute x = 1 into f'(x): f'(1) = 2(1) + 2.
Step 7: Calculate the result: f'(1) = 2 + 2 = 4.
Differentiation – The process of finding the derivative of a function, which represents the rate of change of the function with respect to its variable.
Evaluation of Derivatives – Substituting a specific value into the derivative function to find the slope of the tangent line at that point.
