Let for a real number

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f(x)=e^{(p+1)x}-e^x

for a real number

p>0

. Then the value

x=s_p

for which

f(x)

is minimum is (1)

\frac{-\ln(p+1)}{p}

(2)

-\ln(p+1)

(3)

-\ln p

(4)

\ln\left(\frac{p+1}{p}\right)