Question

The curve $y=a{x}^3+b{x}^2+cx+d$ has a point on inflexion at $x=1$ then;

• A. $a+b=0$
• B. $a+3b=0$
• C. $3a+b=0$
• D. $3a+b=1$

Answer 1

Answer: (C)

$3a+b=0$

$y=a{x}^3+b{x}^2+cx+d$

$\Rightarrow y^{\prime }=3a{x}^2+2bx+c$, differentiate given curve

$\Rightarrow y^{\prime \prime }=6ax+2b$

So for $x=1$ to be inflection point

$y^{\prime \prime }{|}_{x=1}=0$

$\Rightarrow 6a\left(1\right)+2b=0\Rightarrow 3a+b=0$