Find the derivative of the following function using the limiting process.

Question

Find the derivative of the following function  using the limiting process.

Quizplus · Accepted Answer

To find the derivative of the function using the limiting process, we take the limit as the change in x approaches 0 of the difference quotient:

f'(x) = lim (h→0) [f(x+h) - f(x)]/h

Plugging in the given function, we get:

f'(x) = lim (h→0) [(11(x+h)^2 + 5(x+h) - 6) - (11x^2 + 5x - 6)]/h

Simplifying the numerator, we get:

f'(x) = lim (h→0) [11x^2 + 22xh + 11h^2 + 5x + 5h - 6 - 11x^2 - 5x + 6]/h

Canceling out the x^2 and x terms, we get:

f'(x) = lim (h→0) [22xh + 11h^2 + 5h]/h

Factoring out an h from the numerator, we get:

f'(x) = lim (h→0) [h(22x + 11h + 5)]/h

Canceling out the h's, we get:

f'(x) = lim (h→0) 22x + 11h + 5

Plugging in h=0, we get:

f'(x) = 22x + 5

Therefore, the correct choice is A) 11ebbd4d_3ecf_817a_8a0a_8368cc480586_TB8202_11.

Find the Derivative of the Following Function Using the Limiting