If the point (1,3) serves as the point of inflection of the curve y=a x3+b x2 then the value of ' a ' and 'b' are

Question

If the point (1,3) serves as the point of inflection of the curve y=a x3+b x2 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

f prime(x)=3 a x2+2 b x and f prime prime(x)=6 a x+2 b ∴ f prime prime(1)=0 ⇒ 3 a + b =0...(1) also (1,3) lies on the curve ⇒ a + b =3 ldots .(2) solving (1) and (2) we get a =-(3/2) and 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

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

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

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

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

$f^{'} (x) = 3 a x^{2} + 2 b x$ and $f^{''} (x) = 6 a x + 2 b$
$∴ f^{''} (1) = 0 \Rightarrow 3 a + b = 0$ ...(1) also $(1, 3)$ lies on the curve $\Rightarrow a + b = 3 \dots . (2)$
solving (1) and (2) we get $a = - \frac{3}{2}$ and $b = \frac{9}{2}$

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