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+6dy/dx=2x-52x-5=0x=5/2Thus, 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)+6y=99/4Thus, turning point at (5/2,99/4).Additional pointsOnce turning point is identified, you can work out if it is a maximum or minimum by finding d2y/dx2. d2y/dx2<0 - maximumd2y/dx2.>0 - minimumThus for our example aboved2y/dx2=2 - minimum
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