Question

If f (x) = 4x² + 3x - 5, then f(x+h)-f(x)/ h is equal to which of the following?​

Answer 1

`8x + 4h + 3`

Explanation:

`f(x)=4x^2 + 3x-5 \\ \\ f(x+h)=4(x+h)^2+3(x+h)-5 \\ \\ =4(x^2+2xh+h^2)+3x+3h+5 \\ \\ =4x^2+8xh+4h^2+3x+3h+5 \\ \\ f(x+h)-f(x)=(4x^2+8xh+4h^2+3x+3h+5)-(4x^2+3x+5) \\ \\ =8xh+4h^2+3h \\ \\ (f(x+h)-f(x))/(h)=(8xh+4h^2+3h)/(h)=8x+4h+3`