The curve C has the equation: 16y^3 +9x^2y-54x=0, find the x coordinates of the points on C where dy/dx = 0
C: 16y3 + 9x2y -54x = 0 d/dx(16y3) + d/dx(9x2y) + d/dx(-54x) = d/dx(0).............=>48y2.dy/dx + 9x2.dy/dx + y.18x - 54 = 0 dy/dx(48y2+9x2) = 54 - 18xy...........................................=> dy/dx = (54-18xy)/(48y2+9x2) = 0 # dy/dx=0 at turning points therefore: 54-18xy = 0 => y = 3/x # substitute y=3/x into C:=>16.(3/x)3 + 9x2(3/x) -54x = 0 = 432/x3 + 27x -54x = 0 = 432/x3 -27x = 0= 432/x3 = 27x = 432 = 27x4 = 6 = x4 ................................................=> x = 2, -2
EP
Related Maths A Level answers
All answers ▸Why is the derivative of 2^x not x*2^(x-1)?
A 2.4 m long plank of mass 20kg has 2 pins, each 0.5 meters from each respective plank end. A person of mass 40kg stands on the plank 0.1m from one of the pins. Calculate the magnitude of reactions at the pins for this structure to be in equilibrium.
Compute the integral of f(x)=x^3/x^4+1
How would you differentiate 3x^4 - 2x^2 + 9x - 1