Answer:
see explanation
Step-by-step explanation:
(a)
f(x) = 2x + 5 , then difference quotient is
[tex]\frac{2(x+h)+5-(2x+5)}{h}[/tex]
= [tex]\frac{2x+2h+5-2x-5}{h}[/tex]
= [tex]\frac{2h}{h}[/tex]
= 2
(b)
f(x) = 3x² + x , then difference quotient is
[tex]\frac{3(x+h)^2+(x+h)-(3x^2+x)}{h}[/tex]
= [tex]\frac{3(x^2+2hx+h^2+x+h-3x^2-x}{h}[/tex]
= [tex]\frac{3x^2+6hx+3h^2+x+h-3x^2-x}{h}[/tex]
= [tex]\frac{6hx+3h^2+h}{h}[/tex]
= [tex]\frac{h(6x+3h+1)}{h}[/tex]
= 6x+3h+1
