C3 Solomon

For part b, when we are finding the values for f(X) that are are increasing why do we make it greater than or EQUAL to zero


Posted from TSR Mobile

For part b, when we are finding the values for f(X) that are are increasing why do we make it greater than or EQUAL to zero


Posted from TSR Mobile

It's because mathematicians like to make fine and subtle distinctions. Therefore we distinguish between "increasing" (f' greater than or equal to zero) and "strictly increasing" (f' greater than zero).

There are different circumstances where it makes sense to use one of the definitions but not the other.

For a function $f(x)$ to be increasing, we require that its derivative $f'(x) \geq 0$. That should make sense intuitively. The derivative is the gradient and the gradient must always be positive for the function to be increasing. If the gradient (derivative) is negative then the function starts sloping downwards and is hence decreasing. If it's positive, the function is 'angled' upwards and is hence increasing.

Edit: Ah, I misunderstood your question, Gregorious answered it correctly.