Find the derivative of the function by the limit process.

Name: Find the derivative of the function by the limit process.
Brand: Quizplus
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Question

Find the derivative of the function  by the limit process.

Quizplus · Accepted Answer

By using the limit process we have:

f'(x) = lim(h->0) [f(x+h) - f(x)]/h

= lim(h->0) [(4(x+h)^2 + 7(x+h) + 3) - (4x^2 + 7x +3)]/h

= lim(h->0) [4x^2 + 8xh + 4h^2 + 7x + 7h + 3 - 4x^2 - 7x - 3]/h

= lim(h->0) [8xh + 4h^2 + 7h]/h

= lim(h->0) [h(8x+4h+7)]/h

= lim(h->0) 8x + 4h + 7

= 8x + 7

Hence, f'(x) = 8x + 7, which is option D.

Find the Derivative of the Function by the Limit