Question

Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.

Options

• a decreasing function

• an increasing function

• none of these

• a constant function

Answer 1

Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is a decreasing function.

Explanation:

`"f'" ("x") = "sec"^2 "x" - 4 < 0,`

where `"x" in (- pi/3,pi/3).`

`(because "x" in (- pi/3, pi/3) => 1 le "sec x" < 2 => 1 le "sec"^2 "x" < 4)`