The curve C has the equation y = 1/2x^3 - 9x^3/2 + 8/x + 30, find dy/dx. Show that point P(4, -8) lies on C
y = 1/2x^3 - 9x^3/2 + 8/x + 30y = 1/2x^3 - 9x^3/2 + 8x-1 + 30dy/dx = 3/2x^2 - 27/2x^1/2 - 8x^-2 + 0dy/dx = 3/2x^2 - 27/2x^1/2 - 8/x^2substitute x=4 into equation for yy = 1/2(4)^3 - 9(4)^3 + 8/4 +30y = 32 - 72 + 2 + 30y = -8therefore P lies on C
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