differentiation – stationary points - The figure above shows part of the curve C with an equation. y = 3x^{\frac{1}{2}} - x^{\frac{3}{2}} The point A on C is a stationary point and C cuts the x-axis at the point B.

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1: Work out where the graph crosses the axes.

NOTE: The graph will cross the x-axis when y = 0 and the y-axis when x = 0. Substitute in x = 0 and then y = 0 to determine the crossing points, and mark these on your sketch.

EXAMPLE: y = 3x^\frac{1}{2} - x^\frac{3}{2}

0 = 3x^\frac{1}{2} - x^\frac{3}{2}

Step 2: Simplify the equation for the required coordinate.

EXAMPLE: x^\frac{1}{2} (3 - x) = 0

x = 3, x = 0