A curve has equation y = 20x −x2 −2x3 . (A) Find the x-coordinates of the stationary points of the curve.
Firstly, differentiate the equation to find dy/dx.
dy/dx = 20 - 2x - 6x2
As dy/dx represents the gradient, we know that for a stationary point the gradient must be zero, hence for the stationary points, we set dy/dx = 0.
dy/dx = 20 - 2x - 6x2 = 0
Now, we have a quadratic equation, which we can now put into brackets to find our solutions.
dy/dx = 0 = 6x2 - 2x +20 = (x+2)(6x-10)
From these brackets, we know if one set were to be zero, dy/dx would be zero and we will find our x coordinates for our stationary points.
If (x+2) = 0, then x=-2
Or, if (6x-10) = 0, then x=10/6 = 5/3 simplified
BW
Related Maths A Level answers
All answers ▸I don't understand chain rule for differentiation especially when combined with more complex functions.
Two fair six sided dice, called A and B, are rolled and the results are added together. The sum of the dice is 8, what is the probability that two fours were rolled?
Solve these simultaneous equations: 2x+y-5=0 and x^2-y^2=3
Given that d/dx(cosx)=-sinx show that d/dx(secx)=secx(tanx)