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- Find the absolute extrema of the function on the closed interval. f(x) = x2 + 5x, [−4, 0] Ive tried this problem 4 different times the same way my instructor has showed me and just can't get it right.The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. P(x)=-.004x^2+10x-5000Priya is comparing two functions: f(x) = 10 · x² and g(x) = 3 · 2* to find out which one has greater output values as x gets very large. She notices that f(1) = 10 and f(2) = 40. However, g(1) = 6 and g(2) = 12. She concludes that as x continues to grow, the values of f will be greater than the values of g . Explain or show why Priya's conclusion is incorrect.
- 3 determine the value of x of the following piecewise functions please complete solution tyy is a linear function of x with slope −4. If y is −3 when x is −1, what is y when x is 8? You do NOT need to find the linear relationship between x and y to answer this question.Find the points on the graph of the function that are closest to the given point. f(x) = x2 − 4, (0, −2) find: (x,y)= ( , ) Smaller X-value (X,Y)= ( , ) Larger X-value
- Let P=(x,y) be a point on the graph of y=x2-5 a) Express the distance d from P to the origin as a function of x b) what is d if x=0? c) What is d if x=1? I have no idea how to solve this and my book is not very helpful.Suppose that the function y = f(x) is decreasing on the interval [ - 2, 7].(a) Over what interval is the graph of y = f(x + 2) decreasing?(b) Over what interval is the graph of y = f(x - 5) decreasing?(c) What can be said about the graph of y = - f(x)?(d) What can be said about the graph of y = f( - x)?Consider the following. y = 2x3 − 12x2 + 6 (a) Find the critical values of x of the function. (b) determine the relative maxima and minima. (If an answer does not exist, enter DNE.)
- f(x)=(-0.7x2+6.8x+4.2)e-x^2 Find the critical points, inflection points and intercepts (if any) limits as x --> +/- infinityA hat manufacturer is planning to expand its workforce. It estimates thatthe number of hats produced by hiring x new workers is given byT(x) = – 0.25 x4 + 6 x3 0 ≤ x ≤ 18a) When is the rate of change of hat production increasing and when is itdecreasing?b) What is the point of diminishing returns (Hint: inflection point) and themaximum rate of change of hat production?2.Explain why f(x) = x/(x-2) does not have an extreme value on the interval (0,5).