Number of critical points of the function, f(x)=(2/3) √x3-(x/2)+∫ limits1x((1/2)+(1/2) cos 2 t-√t) d t which lie in the interval [-2 π, 2 π] is

Question

Number of critical points of the function, f(x)=(2/3) √x3-(x/2)+∫ limits1x((1/2)+(1/2) cos 2 t-√t) d t which lie in the interval [-2 π, 2 π] is (A) 2 (B) 4 (C) 6 (D) 8

Tardigrade Admin · Accepted Answer

note that f is defined for x >0 f prime( x )=(1/2) cos 2 x =0 ⇒ x = n π ± (π/4) ⇒

Q. Number of critical points of the function, $f (x) = \frac{2}{3} x^{3} - \frac{x}{2} + 1 \int x (\frac{1}{2} + \frac{1}{2} cos 2 t - t) d t$ which lie in the interval $[- 2 π, 2 π]$ is

2

4

6

8

note that $f$ is defined for $x > 0$
$f^{'} (x) = \frac{1}{2} cos 2 x = 0 \Rightarrow x = nπ \pm \frac{π}{4} \Rightarrow$

Q. Number of critical points of the function, f(x)=32​x3​−2x​+1∫x​(21​+21​cos2t−t​)dt which lie in the interval [−2π,2π] is

2

4

6

8

note that f is defined for x>0 f′(x)=21​cos2x=0⇒x=nπ±4π​⇒

Q. Number of critical points of the function, $f (x) = \frac{2}{3} x^{3} - \frac{x}{2} + 1 \int x (\frac{1}{2} + \frac{1}{2} cos 2 t - t) d t$ which lie in the interval $[- 2 π, 2 π]$ is

note that $f$ is defined for $x > 0$
$f^{'} (x) = \frac{1}{2} cos 2 x = 0 \Rightarrow x = nπ \pm \frac{π}{4} \Rightarrow$