HP 39g hp 39g+ (39g & 40g)_mastering the hp 39g+_English_E_F2224-90010.pdf - Page 115

Multiple solutions and the initial guess Our first example was fairly simple because there was only one solution so it did not much matter where we began looking for it. When there is more than one possible answer you are required to supply an initial estimate or guess. The Solve aplet will then try to find a solution which is 'near' to the estimate. Example 1 The volume of a cylinder is given by V = 2π r (r + h) . Find the radius of a cylinder which has a volume of 1 liter and a height of 10cm. Enter the equation into E1 as shown right. When you are entering the equation, ensure that you put a * sign between the R and the bracket. See page 87 for more information on this. Change to the NUM view and enter the known values, remembering that 1 liter=1000cm3. Position the highlight over R, enter a positive value as your estimate, and press to find the solution shown right of 8.57cm. The equation is a quadratic in R which means two solutions are possible. If you enter an initial estimate of -10 you will obtain the negative solution, which is physically invalid in this case. Example 2 If f ( x) = x3 − 2x2 − 5x + 2 find all values of x for which f ( x) = 1 . Although you may have a clear picture in your mind and can provide Solve with the estimates it needs, I'll assume that you would find it helpful to see a graph first. It is also possible to solve this in the Function aplet, which offers more powerful tools. The PLOT view in the Solve aplet, although powerful, can be deceptive if you don't understand it and I sometimes find it easier to work in the Function aplet. In this case we will continue to work in Solve. 115