Mathematics - Application of Derivative Question with Solution | TestHub

If $f^{\prime \prime }(x)<0(>0)$ on an interval $(a,b)$ then the curve $y=f(x)$ on this interval is convex (concave) i.e. it is situated below (above) any of its tangent lines. If ${\mathrm{f}}^{\prime \prime }\left({\mathrm{x}}_0\right)=0$ or does not exist but ${\mathrm{f}}^{\prime }\left({\mathrm{x}}_0\right)$ does exist and the second derivative changes sign when passing through the point $x_0$ then the point $\left(x_0,f\left(x_0\right)\right)$ is the point of inflexion of the curve $y=f(x)$