Find the coordinates of the minimum point on the curve: y = x^2 - x - 2
Start with the given equation from the question and differentiate it with respect to x to give you:dy/dx = 2x - 1The value of this gives you the slope of the curve and we know that the minimum point has a slope of zero. So by setting the differentiated equation to zero and rearranging the equation, the value of x can be found:2x - 1 = 02x = 1x = 0.5This value of x is the x coordinate of the minimum, to then get the corresponding y value, sub this value of x into the equation given in the question:y = x2 - x - 2y = 0.52 - 0.5 - 2 = -2.25So the coordinates of the minimum are (0.5,-2.25)
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