Question

Number of inflection points for the curve $y=x+2x^4$ is

• A. $3$
• B. $1$
• C. $0$
• D. $(n+1{)}^2$

Answer 1

The correct option is C $0$

$y=x+2x^4$
$\frac{dy}{dx}=1+8x^3=0$
$x=-\frac{1}{2}$
$\frac{d^{2}y}{d{x}^2}=24x^2$
$({\begin{array}{c}\frac{d^{2}y}{d{x}^2}\end{array}|}_{x=-\frac{1}{2}}=24(-\frac{1}{2}{)}^2=6>0$
So function has Local minima at critical points
Hence no point of inflection.