Using secant method find all local maxima of the function h(x) = 65 + 20x2 - 20x with the accuracy d = 10-7 Provide: chosen isolation interval, initial points and the number of iterations.
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- Using Fixed-point Iteration Method. Complete the iterations based on the number and relative error. In addition, solve or find g(x) for both functions.Using the equation f(x) = 3.14x2 – 10x + 2 and by using incremental search method, what is the interval of the root at the third iteration where the approximate value of the root was obtained? Start the procedure with the initial value of 0 and a step size of 0.1 (first iteration), then 0.01 (second), and lastly 0.01 (third). Group of answer choices [0.211, 0.212] [0.212, 0.213] [0.213, 0.214] [0.214, 0.215]Using the concept of maxima-minima find three positive numbers, whose sum is 30 and whose product ismaximum
- Minimize the function 2x1^3+4x1x2^3-10x1x2+x2^2 using powell method. use starting point x^0=[5,2]^T. Stop after 4th iteration if you have not reached optimum and state your result.solvefor axis of symmetry and vertex. show work f(x)=-x2-8x+8Using Regula-Falsi method in finding the root of f(x)=x2-8 with an initial guess of [2,3], determine the second root estimate.
- Find the slope of the curve y^2 = 3x + 1 at the point (−1/3, 0). Draw the graph of the curve. (solve by definition/long method)Find two positive numbers whose sum is 110 and whose product is a maximum. (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Use the table to guess the maximum product. (b) Write the product P as a function of x. (c) Use calculus to find the critical number of the function in part (b). Then find the two numbers. (d) Use a graphing utility to graph the function in part (b) and verify the solution from the graph.f(x) = 4x - 1.8x2+1.2x3-0.3x4 Find the maximum using Golden-Section search (Xlower = -2, Xupper= 4 with a percentage error 1%) Show the whole solution for future references
- f(x) = x3 - 2x2 - 15x + 36 = (3 - x)(12 - x - x2) Find the (a) intervals on which f is decreasing and increasing as well as the critical values of f(x), if any; (b) coordinates of local maximum and minimum values (if any); (c) intervals on which f is concave up and concave down as well as the points of inflection, if any; Sketch the graph of and show all details on the graph.Use newtons method to approximate the zeros of the function. continue iterations until 2 successive approximations differ by less than 0.001. Then find the zeros using a graphing utility and compare the results. f(x)=x3-3x-1 show every stepFind the absolute maximum of x40-x20 9n the interval [0,1] .find also it's absolute maximum value