The function y = a(1 - cos x) is maximum when | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the function $y = a(1 - \cos x)$.First,find the derivative $y'$ with respect to $x$:$y' = \frac{d}{dx}[a(1 - \cos x)] = a(0 - (-\sin x)) = a

Vedclass · Accepted Answer

$\pi $

Vedclass · Answer

(A) Given the function $y = a(1 - \cos x)$.First,find the derivative $y'$ with respect to $x$:$y' = \frac{d}{dx}[a(1 - \cos x)] = a(0 - (-\sin x)) = a \sin x$.To find the critical points,set $y' = 0$:$a \sin x = 0 \Rightarrow \sin x = 0 \Rightarrow x = n\pi$ for any integer $n$.Within the standard interval $[0, 2\pi]$,the critical points are $x = 0$ and $x = \pi$.Now,find the second derivative $y''$:$y'' = \frac{d}{dx}(a \sin x) = a \cos x$.Evaluate $y''$ at the critical points:For $x = 0$,$y''(0) = a \cos(0) = a$.For $x = \pi$,$y''(\pi) = a \cos(\pi) = -a$.Assuming $a > 0$,the function has a local maximum when $y'' < 0$,which occurs at $x = \pi$.

The function $y = a(1 - \cos x)$ is maximum when $x = $

Similar Questions

The sum of the maximum and minimum values of the function $f(x) = |5x - 7| + [x^2 + 2x]$ in the interval $[\frac{5}{4}, 2]$,where $[t]$ denotes the greatest integer function $\leq t$,is:

The sum of two nonzero numbers is $4$. The minimum value of the sum of their reciprocals is

$A$ helicopter is flying along the curve given by $y = x^{3/2} + 7, (x \geq 0)$. $A$ soldier positioned at the point $(1/2, 7)$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is

If $p$ and $q$ are respectively the global maximum and global minimum of the function $f(x) = x^2 e^{2x}$ on the interval $[-2, 2]$,then $p e^{-4} + q e^4 =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module