TRUE OR FALSE? If f is differentiable and f'(c)>0 for every c in (a,b), then f is increasing on (a,b). Explain?

It's true. The derivative is the slope of the tangent line at c. If the derivative is negative, then the slope is negative and is f is said to be decreasing. If the derivative is positive, the slope is positive and the function is said to be increasing.