# Let $f$ be differentiable for all $x$. If $f(1)=-2$ and $f'(x)\geq 2$ for $x\in [1,6]$ then

$\begin{array}{1 1}(a)\;f(6)\geq 8&(b)\;f(6)< 8\\(c)\;f(6)< 5&(d)\;f(6)=5\end{array}$

As $f(1)=-2$ and $f'(x)\geq 2\forall x\in [1,6]$
Applying Langrange's mean value theorem