For , define . For which values of does the equation have at least one solution in…

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

Problem

For

a>0

, define

f_a(x)=\ln x - a x

. For which values of

a

does the equation

f_a(x)=0

have at least one solution in the interval

(1,e)

? (a)

0<a\le \dfrac{1}{e}

(b)

0<a<\dfrac{1}{e}

(c)

\dfrac{1}{e}<a<1

(d)

1\le a<e