we have the function
[tex]f(x)=2x^2-9x+5[/tex]Part A
Find out f(x + h)
[tex]\begin{gathered} f\mleft(x+h\mright)=2(x+h)^2-9(x+h)+5 \\ f(x+h)=2(x^2+2xh+h^2)-9x-9h+5 \\ f(x+h)=2x^2+4xh+2h^2-9x-9h+5 \end{gathered}[/tex]Part B
Find out f(x+h)-f(x)
substitute given values
[tex]\begin{gathered} f(x+h)=2x^{2}+4xh+2h^{2}-9x-9h+5 \\ f(x)=2x^2-9x+5 \\ substitute \\ f\mleft(x+h\mright)-f\mleft(x\mright)=(2x^2+4xh+2h^2-9x-9h+5)-(2x^2-9x+5) \\ f(x+h)-f(x)=2x^2+4xh+2h^2-9x-9h+5-2x^2+9x-5 \\ combine\text{ like terms} \\ f(x+h)-f(x)=4xh-9h \end{gathered}[/tex]Part C
Find out [f(x+h)-f(x)]/h
[tex]\frac{f\mleft(x+h\mright)-f\mleft(x\mright)}{h}=\frac{4xh-9h}{h}=4x-9[/tex]