Show that the function f(x) = tan x – 4x is strictly decreasing on [-π/3, π/3]

Dear student

Given that, f(x) = tan x – 4x

Then, the differentiation of the function is given by:

f’(x)= sec^2x – 4

When -π/3 <x π/3,
1<sec x <2

Then, 1<sec^2x <4

Hence, it becomes -3 < (sec^2x-4)<0

Hence, for -π/3 <x π/3,
f’(x)<0

the function f is strictly decreasing on [-π/3, π/3]



Thanks