Functions
Let the function f be differentiable on an interval I containing c. If f has a maximum value at , show that has a minimum value at .
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Using Rolle's Theorem
(a) Let and . Then and . Show that there is at least one value c in the interval where the tangent line to f at is parallel to the tangent line to g at . Identify c.
(b) Let f and g be differentiable functions on [a, b], where and . Show' that there is at least one value c in the interval (a, b) where the tangent line to f at is parallel to the tangent line to g at .
Let I be an interval and f : I â R be differentiable. Show f is decreasing on I if and only if f '(x) ⤠0 for all x â I