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y= 4x³- 3x²- 60x+ 24dy/dx = 12x²- 6x- 60 = 2x²- x- 10 = (2x-5)(x+2)
So stationary points are at x= 5/2 and x= -2
d²x/dy² = 24...

2x2x2x2 = 4x2x2 =8x2=16or(2x2)x(2x2)=(4)x(4)=16

Because of the signs within the equation we know that the factorised solution will be in the form (x+?)(x-?)The two numbers in the brackets have a product of -3 and the sum of -2.In this case, the numbers...

At the points of intersection the x and y coordinates will be the same. So we can solve the equations simultaneously to see what solutions to x and y solve both equations.Rearrange the second equation to ...

The question comes from the quadratic equation r = (-b +- sqrt(b² - 4ac)/2a where r is the root or x coordinate where the line crosses the x-axsis (the y coo...