How do you use the Intermediate Value Theorem to show that the polynomial function #sin2x + cos2x - 2x = 0# has a zero in the interval [0, pi/2]?

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Answer 1 · 2015-09-15T19:44:19

Refer to explanation

First set #f(x)=sin2x+cos2x-2x# then we have that

#f(0)=sin0+cos0-2*0=cos0=1>0#

and

#f(pi/2)=sin(pi/2)+cos(pi/2)-2*(pi/2)=1+0-pi=1-pi<0#

Because #f(0)*f(pi/2)<0# the IVT tells us that #f(x)#

has a zero at #[0,pi/2]#