Question

Let f(x)=8secx. Then f′′(π/9)

Answer 1

f(x)=secx.

f'(x)=sec x tan x.

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

F ' '(x)=(secxtanx)tanx+secx(sec2x).

So, f ' '(x)=secxtan2x+sec3x.

Evaluate:f ' '(π4)=sec(π4)tan2(π4)+sec3(π4)=(√2)(1)2+(√2)3=√2+2√2=3√2.