Find the stationary points of the curve y=2*x^3-15*x^2+24*x+17. Determine whether these points are maximum or minimum.
First, differentiate and put the derivative equal to zero. dy/dx=6x^2-30x+24=0. Solve this equation to get that x=4 and x=1. Substitute these values into the original equation to get the corresponding values of y. The stationary points are (1,17) and (4,-10). Calculate the second derivative to get d^2y/dx^2=12*x-30. When x=1 the second derivative is less than zero so (1,17) is a maximum point and when x=4 the second derivative is greater than zero so (4,-10) is a minimum point.
SM
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