#f'(x_0)=0?# See below.
Given #f:RR->RR# differentiable in #RR# .
Given #a,b# with #a<# #b# for which #f'(a)<0# and #f'(b)>0# . Prove that there is #x_0# #in# #(a,b)# for which #f'(x_0)=0#
Given
Given
1 Answer
Mar 3, 2018
Here is a sketch.
Explanation:
That minimum cannot be at
The minimum occurs at a relative minimum, and be Fermat's Theorem, the derivative at that point is