# Trig Functions: Intercepts, Intervals, and Maximum and Minimum

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Let f be the function defined by f(x)=sin squared x - sinx for 0<or=x<or=(3pi)over 2.

a. find the x- intercepts of the graph of f

b.find the intervals on which f is increasing

c. find the absolute maximum and absolute minimum value of f. Justify your answer.

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This shows how to find x-intercepts, intervals of increase, and absolute maximum and minimum of a trigonometric function.

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Problem:

Let f be the function defined by f(x)=sin squared x - sinx for 0

a. find the x- intercepts of the graph of f

b.find the intervals on which f is increasing

c. find the absolute maximum and absolute minimum value of f. Justify your answer.

Solution:

a. x- intercepts of the graph of f are the x-coordinates of points at which the graph intersects the x-axis.

x-axis is y=0. Thus we are to find x such that

f(x)=sin^2(x )- sinx =0. i.e. sinx(sinx-1)=0. Thus

sinx=0 or sinx =1 Thus the x- intercepts of the graph of f

x=0, pi. and 2*pi here pi=3.14159.. ( you ...

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