The below statements are FALSE. For each statemwt either explain why it is false, give a counterexample, or add tofchange the statement to make it true. I) If! is concave down on an interval, then f" is positive on the same interval. 2) If the top ofa ladder is leaning against a house at a height of h it and the ladder is d sliding down the side of the house at a rate of 1 le. Then if = 1. 3) Let g(x) = Ix]. The Rolle's Theorem tells us that because 9(3) = 90-3), then there exists a point r: E [3.3] such that {To} = O. 5) If: = 5 is a critical number of f (x), then there has to be a maximum or minimum atx=5 6) If the derivative of a function is positive on an interval, then the second derivative of the function must also be positive on the same interval. 7) The Extreme Value theorem says that any function will achieve both an absolute maximum value and an absolute minimum value on an open interval. 1