Question

Consider the function f(x)=6sqrt(x)+1 on the interval [3,5] . Find the average or mean slope of the function on this interval. I FOUND THIS: (6sqrt(5)-6sqrt(3))/2

By the Mean Value Theorem, we know there exists a c in the open interval (35) such that f(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
I NEED C
PLEASE HELP

Answer 1

differentiate f(x) -> f'(x)=3/sqrt(x)(double check) and supposingly that has at least one value equal to mean slope:(6sqrt(5)-6sqrt(3))/2 hence you want to solve: 3/sqrt(x) = (6sqrt(5)-6sqrt(3))/2.

Solve this and you will get x=some value. Put the x=some value back to the original function to get y and you get C (x,y).

Answer 2

Can you please give me the answer to c. I cannot figure it out.

Answer 3

this is homework help, not homework solve. Ask for help is ok, but no one guarrantees to solve your problems. It's your problem after all.