Question
Find a point c satisfying the conclusion of the Mean Value Theorem for the following function and interval.
f(x)=x^ā1 [1,9]
f(x)=x^ā1 [1,9]
Answers
MathMate
f(1)=1/1=1
f(9)=1/9
The mean slope is ((1/9)-1)/(9-1)= -1/9
Now calculate f'(x)=-1/xĀ²
So we need to solve for
f'(x)=-1/9
which gives x=3 or -3.
Since only x=3 is on the interval [1,9], this is the only solution, i.e. c=3.
f(9)=1/9
The mean slope is ((1/9)-1)/(9-1)= -1/9
Now calculate f'(x)=-1/xĀ²
So we need to solve for
f'(x)=-1/9
which gives x=3 or -3.
Since only x=3 is on the interval [1,9], this is the only solution, i.e. c=3.