Explore BrainMass

Explore BrainMass

    Proof using Mean Value Theorem of Continuous, Increasing Functions

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Assume that f and f ' are continuous on [a,b], and f ''(x) exists and f ''(x)>0 for each x

    1) Prove that f ' is increasing on [a,b]
    Hint: the graph is concave up on this interval.

    2) Prove that f(x) f(c) for each x if c and f '(c)=0.

    © BrainMass Inc. brainmass.com March 4, 2021, 7:10 pm ad1c9bdddf


    Solution Summary

    A proof using Mean Value Theorem of Continuous Increasing Functions is provided. The solution is detailed and well presented.