Show that the function f(x) = tan x – 4x is strictly decreasing on [-π/3, π/3]
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Given that, f(x) = tan x – 4x
Then, the differentiation of the function is given by:
f’(x)= sec2x – 4
When -π/3 <x π/3, 1<sec x <2
Then, 1<sec2x <4
Hence, it becomes -3 < (sec2x-4)<0
Hence, for -π/3 <x π/3, f’(x)<0
Therefore, the function “f” is strictly decreasing on [-π/3, π/3]
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