In: Math
Question 1
Let f be a function for which the first derivative is f ' (x) = 2x 2 - 5 / x2 for x > 0, f(1) = 7 and f(5) = 11. Show work for all question.
a). Show that f satisfies the hypotheses of the Mean Value Theorem on [1, 5]
b)Find the value(s) of c on (1, 5) that satisfyies the conclusion of the Mean Value Theorem.
Question 2
Let f(x) = x 3 − 3x 2 . Find intervals where f ' (x) is BOTH positive and decreasing. Show work.