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
Related Maths A Level answers
All answers ▸What is Differentiation?
Statistics: Dave throws a ball at a bucket. The probability the ball goes into the bucket is 0.4. Dave throws the ball four times. What is the probability that he gets it in twice?
The curve C has equation y = x^3 - 3x^2 - 9x + 14. Find the co-ordinates and nature of each of the stationery points of C.
What is the smallest possible value of the integral ∫(x-a)^2 dx between 0 and 1 as a varies?