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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
Application of Derivatives
Solution:
$ f^{\prime}(x)=3 a x^2+2 b x$ and $f^{\prime \prime}(x)=6 a x+2 b$
$\therefore f ^{\prime \prime}(1)=0 \Rightarrow 3 a + b =0$...(1) also $(1,3)$ lies on the curve $\Rightarrow a + b =3 \ldots .(2)$
solving (1) and (2) we get $a =-\frac{3}{2}$ and $b =\frac{9}{2}$