Compare the functions shown below: f(x) cosine graph with points at 0, negative 1 and pi over 2, 1 and pi, 3 and 3 pi over 2, 1 and 2 pi, negative 1 g(x) x y −6 −11 −5 −6 −4 −3 −3 −2 −2 −3 −1 −6 0 −11 h(x) = 2 cos x + 1 which function has the greatest maximum y-value? a. f(x) b. g(x) c. g(x) and h(x) d. f(x) and h(x)

We can find the local maxima and minima of any -continous- function by first finding where the slope is 0, as at this point maxima or minima exist.

Given an arbitrary function '' we find the point of slope 0 by taking its first derivative and equaling to 0 ('').

Lets, first, find the local extremes of the first function:




So our first function has a maxima at '' or at ''.

Now we get the extremes for the second function:




So our second function has a maxima at '' or at ''.

Clearly, '', this means the second function '' has the largest maxima -y value-.