GIven:
[tex]f(x)=-5x+7[/tex]
Required:
To find the value of
[tex]\frac{f(x+h)-f(x)}{h},h\ne0[/tex]
Explanation:
To find the value of f(x+h) we have to substitute (x+h) in the function f(x) instead of 'x'
The simplify with the given question.
[tex]\begin{gathered} f(x+h)=-5(x+h)+7_{} \\ =-5x-5h+7 \end{gathered}[/tex]
Simplifying for the value,
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-5x-5h+7-(-5x+7)}{h} \\ =\frac{-5x-5h+7+5x-7}{h} \\ =\frac{-5h}{h} \\ =-5 \end{gathered}[/tex]
Final Answer:
[tex]\frac{f(x+h)-f(x)}{h}=-5[/tex]
