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- If a rectangle has its base on the x-axis and two vertices on the curve y=e^-x^2, show that the rectangle has the largest possible area when the two vertices are at the points of inflection of the curve.At which iteration shows that the root of a nonlinear equation is Xr = 1.2017 when a = 2 and b = -1 Using bisection method.Find the minimum distance from the parabola x-y2=0 to the point (0,3)(0,3).
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- Find the orthogonal trajectories of the family of curves y6 = k x62. Give an example showing that, even if f0(c) = 0, it could happen that f(x) does not have a localmaximum or minimum at x = c. How is this consistent with Fermat’s Theorem in the book?Find the values of a, b, c and d so that the curve f(x)= ax³ + bx² + cx + d has a local maximum at (-2,4) and a point of inflection at the origin.