Question

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. $a=\frac{3}{2}$ & $b=-\frac{9}{2}$
• B. $a=\frac{3}{2}$ & $b=\frac{9}{2}$
• C. $a=-\frac{3}{2}$ & $b=-\frac{9}{2}$
• D. $a=-\frac{3}{2}$ & $b=\frac{9}{2}$

Answer 1

The correct option is D $a=-\frac{3}{2}$ & $b=\frac{9}{2}$

Given, $y=a{x}^3+b{x}^2$
$y^{\prime }=3a{x}^2+2bx$
$y"=6ax+2b$
for point of inflection $y"=0$
$x=\frac{-b}{3a}\Rightarrow 3a+b=0(asx=1)$
point (1,3) satisfy the curve also,

so $3=a+b$
from (i)& (ii)
$a=-\frac{3}{2},b=\frac{9}{2}$