How do I find the numbers c that satisfy Rolle's Theorem for f(x)=sqrt(x)-x/3 on the interval [0,9] ?

1 Answer
Sep 22, 2014

c=9/4

Let us look at some details.

By taking the derivative,

f'(x)=1/{2sqrt{x}}-1/3

By solving f'(c)=0,

f'(c)=1/{2sqrt{c}}-1/3=0

by adding 1/3,

Rightarrow 1/{2sqrt{c}}=1/3

by taking the reciprocal,

Rightarrow 2sqrt{c}=3

by dividing by 2,

Rightarrow sqrt{c}=3/2

by squaring,

Rightarrow c=9/4