An algebra problem by Md Zuhair

Algebra Level 4

$\large f(x) = \tan x - 4x$

Is the function $f(x)$ above strictly decreasing in the interval $\left(-\dfrac \pi 3, \dfrac \pi 3 \right)$ ?

Cannot be determined No Yes

1 solution

Chew-Seong Cheong
Nov 11, 2016

From $f(x) = \tan x - 4x \implies \dfrac {df(x)}{dx} = \sec^2 x - 4$ . We note that $\dfrac {df(x)}{dx} \in [-3, 0) < 0$ for $x \in \left(-\frac \pi 3, \frac \pi 3 \right)$ , therefore, $f(x)$ is strictly decreasing for $x \in \left(-\frac \pi 3, \frac \pi 3 \right)$ .

An algebra problem by Md Zuhair

1 solution

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