Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (iii) h(x) = sin x + cos x, 0 2 x π < < (iv) f(x) = sin x – cos x, 0 2 < < π
contexto.140
(iii) Given: ……….(i)
and
Now
[Positive]
can have values in both I and III quadrant.
But, therefore, is only in I quadrant.
= [Turning point]
At
=
= = = [Negative]
is a point of local maxima and local maximum value
=
=
(iv) Given: ……….(i)
and
Now
[Negative]
can have values in both II and IV quadrant.
=
= or
or
and [Turning point]
At =
=
=
=
= = [Negative]
is a point of local maxima and local maximum value =
=
= =
At
=
=
=
=
= = [Positive]
is a point of local maxima and local maximum value =