"The range of a$\in$R for which the function f(x) = (4a $-$ 3)(x + loge 5) + 2(a $-$ 7) cot$\left( {{x \over 2}} \right)$ sin2$\left( {{x \over 2}} \right)$, x $\ne$ 2n$\pi$, n$\in$N has critical points, is :"

Question

Accepted Answer

"$$f(x) = (4a - 3)(x + \ln 5) + 2(a - 7)\left( {{{\cos {x \over 2}} \over {\sin {x \over 2}}}.{{\sin }^2}{x \over 2}} \right)$$

$f(x) = (4a - 3)(x + \ln 5) + (a - 7)\sin x$

$f'(x) = (4a - 3) + (a - 7)\cos x = 0$

$\cos x = {{ - (4a - 3)} \over {a - 7}}$

$- 1 \le - {{4a - 3} \over {a - 7}} \le 1$

$- 1 \le {{4a - 3} \over {a - 7}} \le 1$

${{4a - 3} \over {a - 7}} - 1 \le 0$ and ${{4a - 3} \over {a - 7}} + 1 \ge 0$

$\Rightarrow {{ - 4} \over 3} \le a \le 2$"

The range of a$\in$R for which the

function f(x) = (4a $-$ 3)(x + log_e 5) + 2(a $-$ 7) cot$\left( {{x \over 2}} \right)$ sin²$\left( {{x \over 2}} \right)$, x $\ne$ 2n$\pi$, n$\in$N has critical points, is :

Solution

About this question

Drill 25 more like these. Every day. Free.

The range of a$\in$R for which the function f(x) = (4a $-$ 3)(x + loge 5) + 2(a $-$ 7) cot$\left( {{x \over 2}} \right)$ sin2$\left( {{x \over 2}} \right)$, x $\ne$ 2n$\pi$, n$\in$N has critical points, is :

Solution

About this question

More Sets, Relations and Functions questions

Drill 25 more like these. Every day. Free.

The range of a$\in$R for which the

function f(x) = (4a $-$ 3)(x + log_e 5) + 2(a $-$ 7) cot$\left( {{x \over 2}} \right)$ sin²$\left( {{x \over 2}} \right)$, x $\ne$ 2n$\pi$, n$\in$N has critical points, is :