Consider the function f(x)=1/x on the interval [2,9].

Question

Explain process please

Consider the function f(x)=1/x on the interval [2,9].

(A) Find the average or mean slope of the function on this interval.

Average Slope =

(B) By the Mean Value Theorem, we know there exists a c in the open interval (2,9) such that f'(c) is equal to this mean slope. Find all values of c that work and list them (separated by commas) in the box below.

List of values: 

Answer 1

"average slope" = [(1/2)-(1/9)]/(2-7) = -1/18

dy/dx = -1/x²

-1/x² = -1/18 => x=3√2