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- What is the dependent variable and which is the independent variable?Determine the area and construct the normal curve of the following. a. area below z = 2 b. area above z = –1.75 c. –1.5 < z < 1.5If A is the dependent variable and B is the independent variable, then a change in A results in a change in B. 1) True 2) False
- Is the function v(x1,x2)=x21x32 a monotonic transformation of u(x1,x2) ? Select one: a. No b. Yes6). Compute the directional derivative of function f(x,y) = xy³ + 2.x²y at the point (2, 1) in the direction (,, ).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 - y²
- Find the area under the standard normal curve to the left of z=0.21�=0.21. Round your answer to four decimal places, if necessary.Compute the first and second derivatives of the following functions of x. In each case, determine whether the function has any local extremes (maxima or minima) on the domain of nonnegative real numbers – i.e. for x E [0, 0). a. f(x) = 4 + 3x? b. f(x) = x (4x – 3) (9 - 5x) с. f(x) — x2 d. f(x) = In(x) -Convexity & Concavity Consider the function defined by the formula This function is 200 if 0 < x < 20 x y = f(x) = 30- x if 20 ≤x≤40 200 if 40 < x < 60 x a. Concave but not strictly concave b. Strictly convex c. Strictly concave d. Convex but not strictly convex e. I cannot tell because the second derivative of f(x) cannot be calculated
