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 ▸June 2008 C1 Paper Differentiation Question
Core 3: Find all the solutions of 2cos(2x) = 1-2sin(x) in the interval 0<x<360
How do you integrate ln(x)?
Curve D has equation 3x^2+2xy-2y^2+4=0 Find the equation of the tangent at point (2,4) and give your answer in the form ax+by+c=0, were a,b and c are integers.