A curve (C) with equation y=3x^(0.5)-x^(1.5) cuts the X axis at point A and the origin, calculate the co-ordinates of point A.

Insert 0 into the equation in place of Y as the Y co-ordinate is always 0 across the X-Axis.0 = 3x^0.5-x^1.5The x^0.5 can be factored out from the 3x^0.5 and the x^1.5 giving you...x^0.5(3-x^1) = 0 [As x^0.5 multiplied by x^1 is x^1.5, as you add powers when multiplying]So... x^0.5(3-x) = 0 It equals zero when x = 3 as the bracket becomes 0 and anything times 0 is 0.It equals zero when x = 0 as 0 to the power of anything is 0.Therefore the X values when Y = 0 (I.E along the X axis) are 0 and 3. The origin is (0,0) so point A is (3,0)!Remember X values go first followed by Y values in the co-ordinate system. (Along the corridor and up the stairs)