Step-by-step explanation:
Step 1: Find the difference quotient
[tex]f(x+h) = 2(x+h)^2 + 5(x+h)[/tex]
[tex]f(x+h) = 2(x^2+2xh+h^2)+5x+5h[/tex]
[tex]f(x+h) = 2x^2+4xh+2h^2+5x + 5h[/tex]
[tex]f(x) = 2x^2 + 5x[/tex]
Plug it into the formula
Difference Quotient: [tex]\frac{f(x+h)-f(x)}{h}[/tex]
[tex]\frac{2x^2+4xh+2h^2+5x+5h - (2x^2+5x)}{h}[/tex]
[tex]\frac{2x^2 - 2x^2 + 4xh + 2h^2 + 5x - 5x + 5h}{h}[/tex]
[tex]\frac{2h^2+4xh+5h}{h}[/tex]
Pull out an h
[tex]\frac{h(2h+4x+5)}{h}[/tex]
[tex]2h+4x+5[/tex]
Answer: [tex]2h+4x+5[/tex]
