Let
f
be a differentiable function on
[, ]
and
x [, ].
Show that, if
f (x) 0
and
f (x) 0,
then
f
must have a local maximum at
x.
The given information is f(x) has a relative minimum at x = 0. Hence
Now the given equation is:
To find the extremum points we differentiate and equate it to zero
Now for the function y to have a relative minimum ar x=0 we have to have
Hence b can have any values as it is not involved in the derivative function and a must be equal 0 to get a relative minimum for y at x=0.
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