Find each limit by evaluating the derivative of the function

Question

Find each limit by evaluating the derivative of the function

lim_h→0 ((3(2+h)²-(2+h)-10))/h

Answer 1

Let f(x) = 3x² - x    Then f'(x) = 6x - 1, f(2) = 10, and f(2+h) = 3(2+h)² - (2+h)

 

So, the given limit is equivalent to lim_h→0[ (f(2+h) - f(2))/h] = f'(2) = 6(2) - 1 = 11