If the point (1,3) serves as the point of inflection of the curve y = ax 3+ bx 2 then the value of ' a ' and ' b ' are -

Question

If the point (1,3) serves as the point of inflection of the curve y = ax 3+ bx 2 then the value of ' a ' and ' b ' are - (A) a =3 / 2 b =-9 / 2 (B) a =3 / 2 b =9 / 2 (C) a =-3 / 2 b =-9 / 2 (D) a =-3 / 2 b =9 / 2

Tardigrade Admin · Accepted Answer

y=a x3+b x2 y prime=3 a x2+2 b x y prime prime=6 a x+2 b for point of inflection y prime prime=0 x=(-b/3 a) 3 a+b=0(i) ( as x =1) point satisfy the curve also, so 3= a + b.....(ii) from (i) (ii) a =-(3/2), b =(9/2)

Q. If the point $(1, 3)$ serves as the point of inflection of the curve $y = a x^{3} + b x^{2}$ then the value of ' $a$ ' and ' $b$ ' are -

$a = 3/2& b = - 9/2$

$a = 3/2& b = 9/2$

$a = - 3/2& b = - 9/2$

$a = - 3/2& b = 9/2$

$y = a x^{3} + b x^{2}$
$y^{'} = 3 a x^{2} + 2 b x$
$y^{''} = 6 a x + 2 b$
for point of inflection $y^{''} = 0$
$x = \frac{- b}{3 a}$
$3 a + b = 0$ (i) $($ as $x = 1)$
point satisfy the curve also, so
$3 = a + b$ .....(ii)
from (i) & (ii)
$a = - \frac{3}{2}, b = \frac{9}{2}$

Q. If the point (1,3) serves as the point of inflection of the curve y=ax3+bx2 then the value of ' a ' and ' b ' are -

a=3/2&b=−9/2

a=3/2&b=9/2

a=−3/2&b=−9/2

a=−3/2&b=9/2