Finding the Minimum of a Curve and Evaluating a Definite Integral

The mathematical solution explains how to find the coordinates of the minimum point of y = 8x + ¹/_x, for x > 0 and how to find the area between the curve, the x axis and the lines x = 1 and x = 6 using integration. The x value of the minimum point is found by writing the function in index form, differentiating, equating the differential to zero and solving. The second differential is found in order to show that the turning point is a minimum. The value for x is substituted into the original equation to find the y value of the minimum point. To find the required area the function is integrated and evaluated both in terms of natural logarithms and as a decimal. The graphical solution explains how to use the graphic calculator to draw the required graph and find the minimum value. To find the required area, the scales are reset to ensure the required area can be viewed. The functions on the calculator are then used to find the required area and verify the mathematical solution.