A curve is defined for x > 0. The gradient of the curve at the point (x,y) is given by dy/dx = x^(3/2)-2x. Show that this curve has a minimum point and find it.
This is a typical exam style question, taken from an AQA paper. This question is testing your knowledge of stationary points and differentiation. Step 1: Find all stationary points by setting the first derivate to 0, and solving the equation. Step 2: Determine what type of stationary points those we found in step 1 are. This is done by obtaining the second derivative, and substituting in the x values found in step 1. (Optional step 3: interpretationFirst derivative - gradientSecond derivative - rate of change of gradient)
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