Posted by Nathan on Monday, October 28, 2013 at 9:46pm.
Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function.
If there are multiple values, separate them with commas; enter N if there are no such values.
f(x)= x^210x+3, [0,10]

Calculus  Steve, Tuesday, October 29, 2013 at 12:02am
Rolle's Theorem needs f(0) = f(10).
This is true.
So, we know that there is a c such that f'(c) = 0, where 0 <= c <= 10.
f'(x) = 2x10
So, if f'(c) = 0, c=5.
c is indeed in the interval.
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