A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is
JFI. Plot of the provided function.
Answer is $(b)$.
$\implies x=0, 2$
at $x=0, f''(x)=48>0$ it means that $x =0$ is local minima.
but at $x=2, f''(x)=0$ so we can't apply second derivative test. So, we can apply first derivative test.
$f'(1) = 12, f'(3) = 36 $. So, $f'(x)$ is not changing sign on either side of 2. So, $x=2$ is neither maxima nor minima.
So, only one extremum i.e. x=0.
Thank you so much Arjun Sir!