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- 4. Find the maximum values of the following functions and show whether they are maximized at their maximum values. (a) y= f(x)=10x – x² (b) z=10x+10y-xy-x² - y²I need answer typing clear urjent no chatgpt used i will give upvotes2.1 Write a well-commented function program for the function x²e¬ª*, using entry-wise operations (such as .* and .*). To get e" use exp(x). Plot the function on [-5,5] using enough points to make the graph smooth. Turn in the program and the graph.
- Find the inverse of the given function. f(x) = 5x + 4 .... 11 The inverse of the function is f1 (x) = -X. 5 (Simplify your answer. Use integers or fractions for any numbers in the expression.)Consider the linear spline function f(x) = 1 + x + h1(x, 2) where h1(x,2) = x-2 if x>2 and 0 otherwise. What is the slope of f at the point x=-1?Find the derivative and simplify. y = (8x+7)(x² - 3x). y' = Find the derivative and simplify. f'(x) = f(x) = (x12 + 2x4 + 3)(5x³ - 1) For the function y = (x² + 4)(x³ − 9x), at (-3, 0) find the following. (a) the slope of the tangent line (b) the instantaneous rate of change of the function
- Draw a graph of the following function: y= e^x/(1+e^x)Consider the following graph of y = f(x). E D A Which of the following statements about the function f is true? Select one: O f has an endpoint at E and a y-intercept at B. O f has a global maximum at A and a global minimum at C. O f has a critical point at C and a global minimum at D. O f has a global minimum at A and a y-intercept at D.f(x1,x2) 4 2 0 -2 -4 −1 2 0 1 1 0 2 -1 X1 3-2 x2 Figure 2: Graph of the function f(x1, x2) = 2x1 = x²-x+3 Consider the following function: f(x1, x2) = 2x1 - x-x+3. - For your visual convenience, a portion of the function is depicted in Figure 2. (a) Compute the gradient vector of f. (b) Compute the Hessian matrix of f. (c) Determine all points that yield stationary values of f. (d) Use the second-order conditions to determine whether each of the stationary val- ues of f is a maximum, a minimum, or neither.
- Which of the following is true? OA. Quantity rises and the effect on price is unknown B. Quantity is unknown and price rises OC. Quantity rises and price falls OD. Quantity and price rise q4. Verify that a homogenous function has IRS, CRS or DRS depending on whether the degree of the function satisfies y> 1, y = 1, or y< 1.Statement You can select the object to see the slope. Your score depends on the order in which you plot the points. If you plot one point incorrectly and the others correctly, you will receive partial credit for that object. You can adjust the position of the object on the graph without changing its shape by selecting it in between the marked points and moving it around the graph. Connected Points 000 0 Curves 00 0
