Given f(x)=-(x3/3)+x2 sin 1.5 a-x sin a ⋅ sin 2 a-5 arcsin (a2-8 a+17) then

Question

Given f(x)=-(x3/3)+x2 sin 1.5 a-x sin a ⋅ sin 2 a-5 arcsin (a2-8 a+17) then (A) f(x) is not defined at x= sin 8 (B) f prime( sin 8)>0 (C) f prime( x ) is not defined at x = sin 8 (D)  f prime( sin 8)<0

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/7b6618255d5e08abe05764bad6c1ec94-.png" /> f(x)=-(x3/3)+x2 sin 6-x sin 4 ⋅ sin 8-5 sin -1 ((a-4)2+1) f prime( x )=- x 2+2 x sin 6- sin 4 sin 8 ( a =4) f prime( sin 8)=- sin 2 8+2 sin 6 sin 8- sin 4 sin 8 = sin 8[- sin 8+2 sin 6- sin 4] =- sin 8[ sin 8+ sin 4-2 sin 6]=- sin 8[2 sin 6 cos 2-2 sin 6] =2 sin 8 sin 6[1- cos 2]

Q. Given $f (x) = - \frac{x ^{3}}{3} + x^{2} sin 1.5 a - x sin a \cdot sin 2 a - 5 arcsin (a^{2} - 8 a + 17)$ then

$f (x)$ is not defined at $x = sin 8$

$f^{'} (sin 8) > 0$

$f^{'} (x)$ is not defined at $x = sin 8$

$f^{'} (sin 8) < 0$

Q. Given f(x)=−3x3​+x2sin1.5a−xsina⋅sin2a−5arcsin(a2−8a+17) then

f(x) is not defined at x=sin8

f′(sin8)>0

f′(x) is not defined at x=sin8

f′(sin8)<0

f(x)=−3x3​+x2sin6−xsin4⋅sin8−5sin−1((a−4)2+1) f′(x)=−x2+2xsin6−sin4sin8(a=4) f′(sin8)=−sin28+2sin6sin8−sin4sin8 =sin8[−sin8+2sin6−sin4] =−sin8[sin8+sin4−2sin6]=−sin8[2sin6cos2−2sin6] =2sin8sin6[1−cos2]

Q. Given $f (x) = - \frac{x ^{3}}{3} + x^{2} sin 1.5 a - x sin a \cdot sin 2 a - 5 arcsin (a^{2} - 8 a + 17)$ then

$f (x)$ is not defined at $x = sin 8$

$f^{'} (sin 8) > 0$

$f^{'} (x)$ is not defined at $x = sin 8$

$f^{'} (sin 8) < 0$