If $f(x)=e^{x+2}$
, find and simplify the difference quotient $\frac{f(6+h)-f(6)}{h}$
.
A)1
B) $e^{8}-e^{6}$

C) $\frac{e^{x+h}}{h}$

D) $\frac{e^{8}\left(e^{h}-1\right)}{h}$

Question

If $f(x)=e^{x+2}$
 , find and simplify the difference quotient $\frac{f(6+h)-f(6)}{h}$
 .
A)1
B) $e^{8}-e^{6}$

C) $\frac{e^{x+h}}{h}$

D) $\frac{e^{8}\left(e^{h}-1\right)}{h}$

Quizplus · Accepted Answer

The difference quotient is simplified by substituting $f(x) = e^{x+2}$ into the formula, yielding $\frac{e^{6+h+2}-e^{6+2}}{h} = \frac{e^{8+h}-e^{8}}{h} = \frac{e^{8}(e^{h}-1)}{h}$.

If f(x)=ex+2f(x)=e^{x+2}f(x)=ex+2 , Find and Simplify the Difference Quotient f(6+h)−f(6)h\frac{f(6+h)-f(6)}{h}hf(6+h)−f(6)​ A)1 B)

If $f(x)=e^{x+2}$ , Find and Simplify the Difference Quotient $\frac{f(6+h)-f(6)}{h}$
A)1
B)