Mathematics - Application of Derivative Question with Solution | TestHub

For $x$ slightly less than 2, $f(x)=15-x>13$; $f(2)=2(2)-3=1$; for $x$ slightly greater than $2,f(x)=2x-3>1$. So $f(2)=1$ is smaller than all neighbouring values and $x=2$ is a point of local minima; statement 1 is false. The left and right derivatives at $x=2$ are -1 and 2 (and $f$ is not even continuous at $x=2$ ), so $f^{\prime }(2)$ does not exist; statement 2 is true.