**
Math exercise and derivative exercises online : How calculate the x,y coordinate of a point ? How calculate the slope (angular coefficient) of a straight line and the slope of a tangent line using mathematics and derivatives ?
**

Find out the coordinates of the points for which the slope of the tangent line to the curve
*y = x ^{3} - 12x + 1* is zero.

Given *y = f(x) = x ^{3} - 12x + 1*

The derivative of *f(x)* at *x = x _{1}* (and

*f '(x _{1}) = 0 = 3(x_{1})^{2} - 12*

*
3(x _{1})^{2} = 12
*

*
(x _{1})^{2} = 12/3 = 4
*

*
x _{1} = +/- 2
*

*
y _{1} = f(x_{1}) = (+/- 2)^{3} - 12(+/- 2) + 1 = -15 ou 17
*

The slope of the tangent line to the curve is equal to *0* at the point *(2 ; -15)* and at the point *(-2 ; 17)*.

Check this on the following graph :

You can clearly see that both tangent lines have a slope equal to zero because the tangent lines are horizontal at *x = 2* and at *x = -2*.

How can I trace the graph of a function online easily and for free ? Using the online Graph Plotter for free.