If #f(x)=sec(x)#, how do I find #f''(π/4)#?

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Answer 1 · 2015-03-23T11:44:47

First find the expression for #f''(x)#, then evaluate it at #pi/4#.

#f(x)=secx#.

#f'(x)=secxtanx#.

Use the product rule to find #f''(x)#.

#f''(x)=(secxtanx)tanx+secx(sec^2x)#.

So, #f''(x)=secxtan^2x+sec^3x#.

Evaluate:

#f''(pi/4)=sec(pi/4)tan^2(pi/4)+sec^3(pi/4)#

#=(sqrt2)(1)^2+(sqrt2)^3=sqrt2+2sqrt2=3sqrt2#.