Question - Derivative Calculation of a Quadratic Function
Solution:
The image shows a mathematical problem where you are given a function f(x) = 3x^2 + 2x and asked to find the derivative of the function at x = 2, represented as f'(2).To find the derivative f'(x) of the function f(x) = 3x^2 + 2x, we will use the power rule for differentiation. The power rule states that the derivative of x^n is n*x^(n-1).So for f(x) = 3x^2 + 2x:f'(x) = d/dx (3x^2) + d/dx (2x) = 3 * 2x^(2-1) + 2 * 1x^(1-1) = 6x + 2Now we need to evaluate the derivative at x = 2:f'(2) = 6(2) + 2 = 12 + 2 = 14Therefore, the derivative of the function at x = 2, f'(2), is 14.
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