Fanciful shapes can be created by using the implicit plottingcapabilities of computer algebra systems.(a) Graph the curve with equation y(y2 - 1)(y -2) = x(x - 1) (x - 2)At how many points does this curve have horizontaltangents? Estimate the -coordinates of these points.(b) Find equations of the tangent lines at the points (0, 1)and (0, 2).(c) Find the exact -coordinates of the points in part (a).(d) Create even more fanciful curves by modifying theequation in part (a).

Suppose you are climbing a hill whose shape is given by the equation z = 1300- 0.005x² - 0.01y², where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1266). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? Ⓒascend O descend At what rate? 1.6 X descend (b) If you walk northwest, will you start to ascend or descend? O ascend vertical meters per horizontal meter At what rate? (Round your answer to two decimal places.) .57 vertical meters per horizontal meter X (c) In which direction is the slope largest? What is the rate of ascent in that direction? vertical meters per horizontal meter At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.) 60.81

An equation of the line tangent to the graph of x) = x(1-2x)³ at the point (1,-1) is: y = - 7x+6 y = - 6x + 5 y = - 2x + 1 y = 7x- 8

an athlete whose event is the shot put releases a shot. when the shot whose path is shown by the graph to the right is released at an angle of 65°, its height, f(x), in feet, can be modeled by f(x)=-0,04x^2+2.1x+5.2, where x is the shot's horizontal distance, in feet, from its point of release, use this model to solve parts (a) through (c) a. what is the maximum height of the shot and how far from its point of release does this occur?  b. what is the shot's maxium horizontal distance, to the nearest tenth of a foot, or the distanxe of the throw?  c. from what height was the shot released?