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, $45,45,90 : 1,1,sqrt(2)$

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

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

$cos(0)=1$

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

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