Step 2: Find the derivative of the function, which is f'(x). The derivative of e^x is e^x, and the derivative of x^2 is 2x.
Step 3: Combine the derivatives to get f'(x) = e^x + 2x.
Step 4: To find f'(0), substitute 0 into the derivative: f'(0) = e^0 + 2(0).
Step 5: Calculate e^0, which equals 1, and 2(0), which equals 0.
Step 6: Add the results from Step 5: 1 + 0 = 1.
Step 7: Therefore, f'(0) = 1.
Differentiation – The question tests the ability to differentiate a function and evaluate the derivative at a specific point.
Exponential and Polynomial Functions – The function involves both an exponential term (e^x) and a polynomial term (x^2), requiring knowledge of their derivatives.
