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:

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

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

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