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 ▸How do you differentiate by first principles?
A circle with centre C has equation: x^2 + y^2 + 20x - 14 y + 49 = 0. Express the circle in the form (x-a)^2 +(y-b)^2=r^2. Show that the circle touches the y-axis and crosses the x-axis in two distinct points.
Find the equation of the tangent at x=1 for the curve y=(4x^2+1)^3
Curve C has equation x^2 - 3xy - 4y^2 + 64 = 0. a) find dy/dx in terms of x and y. b) find coordinates where dy/dx=0.