If f(x)= sec x, then find f " (pie/4)?

Question

If f(x)= sec x, then find f " (pie/4)

Answer 1

f(x)= sec x

f'(x) = sec x tan x

f''(x)= sec x d/dx(tan x) + tan x d/dx(sec x)

f''(x)= sec x * sec ^2(x)+ tan x * sec x tan x

f"(x)= sec ^3 x + tan ^2x sec x

f"(pie/4)= sec ^3(pie/4) + tan ^2(pie/4) sec (pie/4)

f"(pie/4)= 2* (2^(1/2)) + 1^2* 2^(1/2)

so ans is

2.82 + 1.4
= 3.22

Answer 2

f'(x) = sec x tan x
By the Product Rule,
f''(x) = sec x tan x (tan x) + sec x tan x (sec^2 x)
f''(x) = sec x tan^2 x + sec^3 x tan x
f"(pie/4) = 3 sqrt 2

Answer 3

sec(x) = 1/cos(x)
then take second derivative and plug and chug