Understanding the Use of the Long Jump Formula R=9.21m and Its Derivation

[rudransh verma]

My post was intended as self evident.

It’s not obvious if that you mean

 

[jbriggs444]

You mean when there is no rate + or - then the function is either at its maximum or minimum.

Be careful. The implication is the other way around.

If the rate is + or - then the function is not at its maximum or minimum.
If the rate is 0 then the function might be at a maximum or minimum.

Take the example of $f(x) = x^3$. The first derivative of this function is zero at $x=0$ but there is no maximum or minimum there.

The function is increasing/decreasing at an instant if the derivative is not equal to zero.

Yes. This statement is correct.

If the derivative is non-zero, the function is increasing or decreasing and, therefore, is not at a maximum or minimum. Intuitively, it is like climbing a hill. If the ground is sloping, you are not at the top yet.

Here is an on-line lesson.