Let a < b. Suppose a function f is defined on [a, b] and the
derivative f'(x) exists for all x ∈ [a, b]. If f'(a) < 0 and
f'(b) > 0. Show that there exists a point c, a < c < b,
such that f'(c) = 0.
Let A B Suppose A Function F Is Defined On A B And The Derivative F X Exists For All X A B If F A 0 An 1 (25.37 KiB) Viewed 14 times
(20 marks) Let a < b. Suppose a function f is defined on [a, b] and the derivative f'(2) exists for all z € [a, b]. If f'(a) < 0 and f'(b) > 0. Show that there exists a point c, a<c<b, such that f'(c) = 0.
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