Which of the following best explains why the graph of is concave upward on the interval ?

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Which of the following best explains why the graph of

y=\tan x

is concave upward on the interval

(0,\,\pi/2)

? (a) Because

y''=\sec^2 x

, which is always positive on

(0,\pi/2)

. (b) Because

y'=\sec^2 x

is positive on

(0,\pi/2)

, so the curve bends upward. (c) Because

y''=2\sec^2 x\tan x

, and both

\sec^2 x

and

\tan x

are positive on

(0,\pi/2)

. (d) Because

y''=2\sec x\tan x

, and both

\sec x

and

\tan x

are positive on

(0,\pi/2)