Question

Find each of the following for f(x) = 2x² - 9x + 5.(A) f(x + h)(B) f(x+h)-f(x)(C)f(x+h)-f(x)h

Answer 1

we have the function

`f(x)=2x^2-9x+5`

Part A

Find out f(x + h)

`\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}`

Part B

Find out f(x+h)-f(x)

substitute given values

`\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}`

Part C

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

`(f\mleft(x+h\mright)-f\mleft(x\mright))/(h)=(4xh-9h)/(h)=4x-9`