Question

Find the difference quotient f(x)=2x^2+5x

Answer 1

Answer:

4x + 2h + 5

Step-by-step explanation:

[f(x+h) - f(h)] / h

{[2(x + h)² + 5(x + h)] - (2x² + 5x)} / h

{2x² + 4xh + 2h² + 5x + 5h - 2x² - 5x} / h

[4xh + 2h² + 5h]/h

4x + 2h + 5

Answer 2

Step-by-step explanation:

Step 1:  Find the difference quotient

$f(x+h) = 2(x+h)^2 + 5(x+h)$

$f(x+h) = 2(x^2+2xh+h^2)+5x+5h$

$f(x+h) = 2x^2+4xh+2h^2+5x + 5h$

$f(x) = 2x^2 + 5x$

Plug it into the formula

Difference Quotient:  $\frac{f(x+h)-f(x)}{h}$

$\frac{2x^2+4xh+2h^2+5x+5h - (2x^2+5x)}{h}$

$\frac{2x^2 - 2x^2 + 4xh + 2h^2 + 5x - 5x + 5h}{h}$

$\frac{2h^2+4xh+5h}{h}$

Pull out an h

$\frac{h(2h+4x+5)}{h}$

$2h+4x+5$

Answer:  $2h+4x+5$