for the function f(x)=5x² - 5x, evaluate and simplify. (f(x + h)-f(x))/h question help: video message…

Explanation:

Step1: Find (f(x + h))

Substitute (x+h) into (f(x)): [ \begin{align*} f(x + h)&=5(x + h)^2-5(x + h)\ &=5(x^{2}+2xh+h^{2})-5x - 5h\ &=5x^{2}+10xh+5h^{2}-5x - 5h \end{align*} ]

Step2: Calculate (f(x + h)-f(x))

[ \begin{align*} f(x + h)-f(x)&=(5x^{2}+10xh+5h^{2}-5x - 5h)-(5x^{2}-5x)\ &=5x^{2}+10xh+5h^{2}-5x - 5h - 5x^{2}+5x\ &=10xh+5h^{2}-5h \end{align*} ]

Step3: Calculate (\frac{f(x + h)-f(x)}{h})

[ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{10xh+5h^{2}-5h}{h}\ &=\frac{h(10x + 5h-5)}{h}\ &=10x+5h - 5 \end{align*} ]

Answer:

(10x+5h - 5)