1. [-/1 Points] DETAILS LARCALCET7 4.1.008.MI. Find the value of the derivative (if it exists) at the indicated extremum, (If an answer does not exist, enter DNE.) -2, 10v3 (x) = - 5xVx + 1 F (=2) = -2 Need Help? Read It Watch it Master It Submit Answer 2. [-/1.25 Points] DETAILS LARCALCET7 4.1.011. Approximate the critical numbers of the function shown in the graph. Determine whether the function has a relative maximum, a relative minimum, an absolute maximum, an absolute minimum, or none of these at each critical number on the interval shown. (Enter your answers as a comma-separated list.) Approximate the critical numbers. List the critical numbers at which each phenomenon occurs. (If an answer does not exist, enter DNE.) relative maxima x = relative minima X absolute maxima x = absolute minima x = Need Help? Read It Watch It3. [-/1 Points] DETAILS LARCALCET7 4.1.015.MI. Find the critical numbers of the function. (Enter your answers as a comma-separated list.) (x) = 3x7 - 4x x = Need Help? Read It Watch it Master It Submit Answer 4. [-/1 Points] DETAILS LARCALCET7 4.1.025. Find the absolute extrema of the function on the closed interval. Rx) = 6 - x, [-3, 4) minimum (x, y) =( maximum (x, y) = ( Need Help? Read It Watch It Submit Answer 5. [-/1 Points] DETAILS LARCALCET7 4.1.035. Find the absolute extreme of the function on the closed interval. y = 2 - It - 21. [-9, 4 minimum (t, y) = ( maximum (t, y) = ( Need Help? Read It Watch It Submit Answer 6. [-/1.5 Points] DETAILS LARCALCET7 4.1.039.MI. Find the absolute extreme of the function on the closed interval. y = 7 cos x, [0, 2m] minimum (x, y) = ( maximum (x, y) = (smaller x-value) (x, y) = ( ) (larger x-value) Need Help? Read It Watch it Master It Submit Answer7. [-/2 Points] DETAILS LARCALCET7 4.1.049. MY Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.) R(x) = x2 - 4x (a) [-1, 4] minimum (x, y ) = maximum (x, y) = (b) (2, 5] minimum (x, y ) = ( maximum (x, y) = (c) (0, 4) minimum (x, y) = ( maximum (x, y) = ( (d) [2, 6) minimum (x, y ) = ( maximum (x, y) = Need Help? Read It Watch it Submit Answer 8. [-/1.5 Points] DETAILS LARCALCET7 4.1.072. A lawn sprinkler is constructed in such a way that de/dr is constant, where 8 ranges between 450 and 1350 (see figure).+ The distance the water travels horizontally is sin(20) 32 45 5 0 5 135 where the constant v is the speed of the water. Find dx/dt and explain why this lawn sprinkler does not water evenly. What part of the lawn receives the most water? 8 = 105 = 750 6 = 135 4 10 -45 64 Water sprinkler. 45* $ $ 1350 Find dx/dt. (Consider that de/dt = c,and enter your answer in terms of c.) dx = what part of the lawn receives the most water? O the inner part O the outer part9. [-/5.5 Points] DETAILS LARCALCET7 4.1.074. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In order to build a highway, it is necessary to fill a section of a valley where the grades (slopes) of the sides are p% and 9%, where p = 6 and q = 4 (see figure). The top of the filled region will have the shape of a parabolic arc that is tangent to the two slopes at the points A and B. The horizontal distances from A to the y-axis and from B to the y-axis are both 500 feet. * 500 ft 500 # - Highway of grade Nor drown to reale (a) Find the coordinates of A. (x, y) = ( Find the coordinates of B. (x, y) = ( (b) Find a quadratic function y = ax? + bx + c for -500 s x s 500 that describes the top of the filled region. (c) Construct a table giving the depths d of the fill for x = -500, -400, -300, -200, -100, 0, 100, 200, 300, 400, and 500. (Round your answers to two decimal places.) * -500 -400 -300 -200 -100 10 | 200 300 400 500 (d) what will be the lowest point on the completed highway? (x, y) = ( Will it be directly over the point where the two hillsides come together? Yes No Need Help? Read It Watch It Submit