Question

Let f(x)=−4−3x+2x^2. Use the limit definition of the derivative to find find f�Œ(a)

Answer 1

lim(h->0) f(x+h)-f(x))/h

2(x+h)^2 -3(x +h)- 4 - (2x^2 -3x -4))/h

2(x^2 + xh + xh + h^2 ) - 3x -3h -2x^2 + 3x + 4))/h

( 2x^2 + 4xh + 2h^2 -3x -3h -4-2x^2 +3x +4))/h

(4xh +2h^2 -3h))/h

h(4x + 2h -3)/h

lim(h->0) (4x +2h -3) = 4x +2(0) -3 = 4x -3