Step 1: Start with the function f(x) = 5x^2 - 3x + 7.
Step 2: To find the first derivative f'(x), use the power rule. The derivative of 5x^2 is 10x, and the derivative of -3x is -3. The constant 7 has a derivative of 0.
Step 3: Combine the results from Step 2 to get f'(x) = 10x - 3.
Step 4: Now, to find the second derivative f''(x), take the derivative of f'(x). The derivative of 10x is 10, and the derivative of -3 is 0.
Step 5: Combine the results from Step 4 to get f''(x) = 10.
Differentiation – The process of finding the derivative of a function, which measures how the function changes as its input changes.
Second Derivative – The derivative of the first derivative, which provides information about the curvature or concavity of the original function.
