How do I find the average rate of change of #f(x) = sec x# from 0 to #pi/4#?

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Answer 1 · 2014-09-19T01:12:57

Average rate of change = #(f(b)-f(a))/(b-a)#, where #b# is the upper bound and #a# is the lower bound.

#f(x) = sec x#

#(f(pi/4)-f(0))/(pi/4-0)=(sec(pi/4)-sec(0))/(pi/4)=(sqrt(2)-1)/(pi/4)=0.4142/0.7854=0.5274#

Things to remember:

Review the unit circle

#pi/4= 45#, degrees and is a special triangle, #45,45,90 : 1,1,sqrt(2)#

#cos (pi/4)=1/sqrt(2)#

#sec (pi/4)=1/(cos (pi/4))=1/(1/sqrt(2))=1/1*sqrt(2)/1=sqrt(2)/1=sqrt(2)#

#cos(0)=1#

#sec (0)=1/(cos (0))=1/(1)=1#