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How do I find the turning points of a curve?

At turning points, the gradient is 0. Differentiating an equation gives the gradient at a certain point with a given value of x. To find turning points, find values of x where the derivative is 0.

Example:

y=x2-5x+6

dy/dx=2x-5

2x-5=0

x=5/2

Thus, there is on turning point when x=5/2. To find y, substitute the x value into the original formula. 

y=(5/2)2-5x(5/2)+6

y=99/4

Thus, turning point at (5/2,99/4).

Additional points

Once turning point is identified, you can work out if it is a maximum or minimum by finding d2y/dx2. 

d2y/dx2<0 - maximum

d2y/dx2.>0 - minimum

Thus for our example above

d2y/dx2=2 - minimum

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