Suppose that f(t) =t +5t-2. (a) What is the average rate of change of f(t) over the interval 2 to 3? (b) What is the (instantaneous) rate of change of f(t) when t 2? The average rate of change of f(t) over the interval 2 to 3 is (Simplify your answer.) The (instantaneous) rate of change of f(t) when t= 2 is (Simplify your answer.)
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- Colton is trying to figure out when two buses traveling at different speeds will pass one another. The buses are traveling in the same direction and begin 3 miles apart. He has defined variable tt as follows: Let tt represent the time in hours. Is this a good variable definition? YES OR NO ? IF NO than explain why?A company estimates that it will sell N(x) units of a product after spending $x thousand on advertising, as given by N(x)= -0.25x +22x³-472.5x² +83,000, where 21 ≤x≤45. When is the rate of change of sales increasing and when is it decreasing? What is the point of diminishing returns and the maximum rate of change of sales? Graph N and N' on the same coordinate system. The rate of change of sales is increasing on. (Type your answer in interval notation.) The rate of change of sales is decreasing on (Type your answer in interval notation.) The point of diminishing returns is thousand dollars. The maximum rate of change of sales is sales per thousand dollars. (Round to the nearest whole number as needed.) Graph N and N' on the same coordinate system. Choose the correct answer below. OA. Av 110000 0+ 16 N N' 50 Q Q G OB. 110000 Ay 0+ 16 N N' 50 Q Q O C. Ay Q Q MN 110000 04 16 N N' + O D. 50 110000 Ay 0+ 16 N N' X 50 Q GFind 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.)
- 6). Compute the directional derivative of function f(x,y) = xy³ + 2.x²y at the point (2, 1) in the direction (,, ).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) -Evaluate the integral. (Use C for the constant of integration.)
- A kids' organization sold 570 bars last year at $ 2.55 per candy bar. Research has suggested that for each $ 0.25 price increase, they will sell 20 less candy bars. They want to know what price should they sell their candy bars at to maximize their revenue. Please help them out, showing your work neatly in the following steps. And please label the steps clearly with the letters A through F A) Define your variables. This means that for every letter you use to represent a value, you communicate what it equals in words. B) Find the linear equation that relates the price and the number sold. C) Determine a function that represents the Revenue. (Remember, Revenue = (Price)*(Number Sold)). D) Graph your revenue function on your calculator or Desmos or something similar and on your paper, labeling the axes and the maximum point. E) Uusing your calculator or Desmos or something similar, use your graph to determine the price that maximizes the revenue for the organization. Do NOT use calculus…Traders often buy foreign currency in the hope of making money when the currency’s value changes. For example, on April 15, 2015, one U.S. dollar could purchase 0.9428 euro, and one euro could purchase 126.457 yen. Let f(x) represent the number of euros you can buy with x dollars, andlet g(x) represent the number of yen you can buy with x euros.(a) Find a function that relates dollars to euros.(b) Find a function that relates euros to yen.(c) Use the results of parts (a) and (b) to find a function that relates dollars to yen. That is, find (g ∘ f) (x) = g(f(x) ).(d) What is g(f(1000) )?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?
- Graph the function C=50+0.8Y and give economic interpretations of the elements of the equation.You are given the function y=11−1.5x. The slope of the equation is enter your response here. (Round your answer to one decimal place.)quiz 1 (page 1 of 5) 105 econ مبادئ في الاقتصاد الرياضی ش 2 و ش elearning yu.edu.jo Question 1 Not yet answered Question 3 Marked out of 1.00 Not yet answered Marked out of 1.00 **Assume that you have the following equations: Simplify the following expression: 3X(8x+9)- X(X+7) 4P+4Q=16 2P-Q=2 The equilibrium price is: O a. 23x2 + 20X O a. P=5 O b. X2-30X O b. P=6 O c. 25X2 + 32X Oc. P-2 d. 21X2-24X O d. P-4 e. None of the above O e. None of the above Clear my choice Clear my choice Next page Next page Quiz navigation Quiz navigation 12 31 4 ...