The slope of a curve at a certain point is the same as the slope of the line that is tangent to the curve at that point (touches the curve at ONE point and does not cross over the curve). This is also the derivative. Therefore, to find the derivative of a curve at point "P", you can simply draw the tangent line and find its slope with the equation:

m of P= 

OR you can take the derivative of the equation and plug in the X and Y values of point P on the curve f(x):

P=(6,4)

f(x)=-x2+9x-14

f'(x)=-2x+9..... (you get this using the formula f'(x)=nx^(n-1))

...SO you then find the slope of the curve at (6,4) by finding the derivative at P:

f'(6)=

This means that when a curve has a tangent of zero, there is a maximum or minimum, or the graph is horizontal. When there is no derivative (the denominator in equation above is zero), there is