Mathematics - Application of Derivative Question with Solution | TestHub

The product is negative and $f^{\prime \prime }\left(c_1\right)>f^{\prime \prime }\left(c_2\right)$, so $f^{\prime \prime }\left(c_1\right)>0>f^{\prime \prime }\left(c_2\right)$ : local minimum at $c_1$ (value 5 ), local maximum at $c_2$ (value 0 ). Just right of $c_1,f>5$; just left of $c_2,f<0$. So $f$ rises from $c_1$ to a local maximum inside $\left(c_1,c_2\right)$, then falls below 0 to a local minimum inside $\left(c_1,c_2\right)$, then rises to 0 at $c_2$. Two extra roots of $f^{\prime }$ in $\left(c_1,c_2\right)$ plus $c_1,c_2$ give at least 4.