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C2 Differentiation

Find the co-ordinates of the points where the gradient is zero on the curve with equation:

y = x^2 +54/x

Any help is very much appreciated

Reply 1

k@tie

y=x^2 + 54X^-1
dy/dx = 2x -54x^-2
0 = 2x -54x^-2
0 = 2x^3 - 54
54 =2x^3
x^3 = 27
x=3 y=25

Reply 2

nas7232

Find the co-ordinates of the points where the gradient is zero on the curve with equation:

y = x^2 +54/x

Any help is very much appreciated

y = x^2 + 54x^-1

dy/dx = 2x + (-54x^-2)

2 x 3 - 54/9 = 0
when x = 3, dy/dx = 0

Therefore, the gradient is 0 at this point.
y = 3^2 - 54/3 =

(3,-9)

Use this way of working it out, you can get some more points if there are any left, should be 1 or 2 more co-ordinates left.