Mean Value Theorem

Question

Function f(x)=1/x on the interval [4,9]. Find the average/mean slope of the function on this interval. Then f'(c) is equal to the mean slope, find c

my work:

a) f(x)=1/x

((1/9)-(1/4))/(9-4)= -1/36

b) f'(c)=1/x^2

1/x^2= -1/36 Is this set up right and if so where do I go from here?

Answer 1

You are missing a minus sign. The derivative of 1/x is -1/x²

So -1/x² = - 1/36 So x = 6. And so c = 6 (which is between 4 and 9

Answer 2

Almost right!

The derivative of 1/x = -1/x²

So -1/x² = -1/36

then solve for x which is the value of c you need.