This function is infinitely differentiable on entire The necessary condition of extremum for such a function is
To find the derivative of this function we need the product rule and the derivatives of sine, cosine, hyperbolic sine and hyperbolic cosine. We know them:)
So
The function is always positive, hence
at those points where
They are
for integer
and three of them are in the given interval:
and
Moreover, has the same sign as
so it is positive from
to
negative from
to
positive from
to
and negative again from
to
Function
increases and decreases accordingly, therefore it has local minima at
and
and local maxima at
and
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