Find the range of the values for for which is strictly increasing.
Use the quadratic formula, pay attention in particular to the discriminant.
Think about what it means to have f'(x) > 0. It means if you graph f'(x), you should have every single point above the x axis => no real roots.
So under what conditions does a quadratic equation not have real roots?
but tell me one thing....here we are considering the non-existence of any real root of the quadratic equation because we have a condition. but in case we had the function decreasing, then also we would have considered the same criterion, that is, the non-existence of any real root; and hence the final answer (ie, c > 1) would be the same.
how can you explain this?