increasing function?

Question

Is an increasing or decreasing function the same as increading/decreasing slope?

Answer 1

As you have stated it, no, not quite. An increasing function is one which has a positive slope. If the slope is increasing - i.e. the second derivative is positive - that doesn't mean that the slope itself is positive. In other words, a function may be decreasing with an increasing slope - in that case, it's heading down but turning upwards. It may be increasing with an increasing slope - it's heading up and getting steeper. Or any other combination you can think of.

In short - increasing function, the line is heading up. Increasing slope, the line is curving upwards.

Answer 2

An increasing/decreasing slope would be where the derivative of a function is positive or negative over the slope.

An increasing function is one that is generally increasing from left to right.y = x