1. Find the derivatives of the following: a. y = 8x3 b. у%3-12 c. f(x) = -6x5 d. y = 5x-2 e. y = -9x-4 2. What is the slope of the function y 0.2x* when x 3?
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- The line in the graph shows a relationship between two variables, x and y. What is the slope of the curve? ... The slope of the curve is >>> If the slope is negative, use a minus sign. If the slope is positive, do not use a plus sign. 8 7 5- 4- 3- 2- 1- 0- y 0 1 2 3 4) Find and classify the stationary points of the following function: f (x) = 1. [Specify the 1st and 2nd order conditions.] 1. T-16). Compute the directional derivative of function f(x,y) = xy³ + 2.x²y at the point (2, 1) in the direction (,, ).
- 5. Find all stationary points of the following function. For each stationary point, determine if it is a local maxima, a local minima, or neither. y = (x + 1)6 + (x + 1)7.Graph the function C=50+0.8Y and give economic interpretations of the elements of the equation.A rental car company has a special deal on one of the available rentals. Let C be the cost, in dollars, of the rental car as a function of the distance d, in miles, it is driven in one day. A. What would the value C(75) represent in this context? B. Is function Cincreasing or decreasing? What are the units of the slope in this situation? C. Identify any maximum or minimum values of the function. What do they represent in this situation? State any assumptions that you make. D. Would the graph of C have any intercepts? What would they represent in this situation? E. Write a rule for C(d), and sketch a graph of the function.
- Obtain the second derivative of the function: y = 2 – 5x4 + 3/2x2Compute 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) -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.)
- The following graph contains four lines (A, B, C and D), each of which has a slope that is either positive, negative, zero, or infinite. Y-axisX-axisBDCA For each of the following scenarios, indicate whether the relationship between the two variables is positive or negative, as well as which line on the previous graph has a slope that reflects this type of relationship. Hint: The X-axis and Y-axis on the graph are not labeled intentionally. You need to substitute the variables from each scenario for the horizontal and vertical axis. For example, in the first scenario, X-axis should be labeled “ ice-cream" and Y-axis should be labeled "The temperature". Scenario Relationship Line As the temperature rises, the demand for ice-cream rises. Negative As the temperature rises, the demand for hot cocoa falls. Positive As the temperature falls, the demand for popsicles falls. Negative True or False: Line B has a slope of infinity.…Consider the function Y = *square root*pXZ where X > 0 and Z > 0. Draw the contour lines (in the positive quadrant) for this function for Y = 4, Y = 5, and Y = 10. What do we call the shape of these contour lines? Where does the line 20X + 10Z = 200 intersect with the contour lineY = 50?Please find the effect of Y and r if there is a decrease in the tax rate. Use the following equations and evaluate the total derivative.
