Mathematics - Application of Derivative Question with Solution | TestHub

Given $f(1)=-2$ and $f^{\prime }(x)\ge 4.2$ for $1\le x\le 6$ Consider $f^{\prime }(x)=\frac{f(x+h)-f(x)}{h}$ $\Rightarrow f(x+h)-f(x)=f^{\prime }(x)\cdot h\ge (4.2)h$ So, $f(x+h)\ge f(x)+(4.2)h$ put $x=1$ and $h=5$, we get $f(6)\ge f(1)+5(4.2)\Rightarrow f(6)\ge 19$ Hence $f(6)$ lies in $[19,\infty )$