for the function $f(x)=x^{2}+8$, construct and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$…
for the function $f(x)=x^{2}+8$, construct and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$. the difference quotient is
Answer
Explanation:
Step1: Find ( f(x + h) )
Substitute ( x+h ) into ( f(x)=x^{2}+8 ). ( f(x + h)=(x + h)^{2}+8=x^{2}+2xh+h^{2}+8 )
Step2: Calculate ( f(x + h)-f(x) )
( f(x + h)-f(x)=(x^{2}+2xh+h^{2}+8)-(x^{2}+8) ) ( =x^{2}+2xh+h^{2}+8 - x^{2}-8=2xh + h^{2} )
Step3: Simplify ( \frac{f(x + h)-f(x)}{h} )
( \frac{f(x + h)-f(x)}{h}=\frac{2xh + h^{2}}{h}=\frac{h(2x + h)}{h}=2x+h )
Answer:
( 2x + h )