Question

For the function f(x)=5x2−5x, evaluate and simplify.

Answer 1

9514 1404 393

Answer:

  10x -5 +5h

Step-by-step explanation:

Use the function definition with the given arguments.

  $\dfrac{f(x+h)-f(x)}{h}=\dfrac{(5(x+h)^2-5(x+h))-(5x^2-5x)}{h}\\\\=\dfrac{(5(x^2+2hx+h^2)-5(x+h))-(5x^2-5x)}{h}\\\\=\dfrac{5x^2+10hx+5h^2-5x-5h-5x^2+5x}{h}=\dfrac{10hx-5h+5h^2}{h}\\\\=\boxed{10x-5+5h}$