Use the given parameters to answer the following questions. If you have a graphing device, graph the curve to check your work.
x = 2t3 + 3t2 - 120t
y = 2t3 + 3t2 + 4
(a) Find the points on the curve where the tangent is horizontal.
(b) Find the points on the curve where the tangent is vertical.
Use the given parameters to answer the following questions. If you have a graphing device, graph the curve to check your work. x = 2t3 + 3t2 - 120t y = 2t3 + 3t2 + 5 (a) Find the points on the curve where the tangent is horizontal. (b) Find the points on the curve where the tangent is vertical.
Use the given parameters to answer the following questions. If you have a graphing device, graph the curve to check your work. x = 2t3 + 3t2 - 36t y = 2t3 + 3t2 + 1 (a) Find the points on the curve where the tangent is horizontal. (b) Find the points on the curve where the tangent is vertical.
Find the tangent equation to the given curve that passes through the point (4, 3). Note that due to the t2 in the x equation and the 3 in the y equation, the equation in the parameter t has more than one solution. This means that there is a second tangent equation to the given curve that passes through a different point. x = 3t2+1 y = 2t3 + 1 y = (tangent at smaller t) y = (tangent at larger t)
4. Tired from the long week, with the amusement park and the wok and dinner plate designs, you retreat to be in peace and study parametric equations. A curious leaflike curve called the "folium of Descartes" catches your eye; it is defined by the parametric equations 3t 3t2 (a) (4 points) Show that if the point (a, b) lies on the curve, then so does (b, a); that is, the curve is symmetric with respect to the line y a....
Given the parametric curve x = 3t – tº, y = 3ta. (a) Find all x and y intercepts. (b) Find all points (x, y) where there is a vertical or horizontal tangent. (c) Put this information together in a chart to determine the intervals of increase and decrease and use this to sketch the curve.
2. Use the information in the charts to answer the following questions and sketch the graph of the function f(x) a) List all the critical points (both coordinates) and classify them as max, min, or neither b) List all the inflection points - ND + + ND - 0 + S. Sketch the graph of each given function by doing the following (box your answer to each of the questions) 1. Determine the domain of the function. Use limits to...
Find the points (x,y) on the curve C given by x = 1+t? and y = t- t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes.
8) Find the points (x,y) on the curve C given by x = 1+ t2 and y = t – t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes. Suggestion: On Desmos, let -2 st s 2 to see the full curve and to estimate where these points are. Points
Chapter 4 tch the graph. Each part Use the function below on the interval specified to answer the following questions and ske counts equally. f(x)= ex sin(x), [-π, π] a. Find any x- and y-intercepts for the specified interval. Show work. b. Find any horizontal and vertical asymptotes. Show work. c Give the intervals in interval notation where the function is increasing and where it is decreasing for the specified interval. Show your work. You may show your work in...
8) Find the points (x,y) on the curve given by x = 1+t2 and y=t-t3 where the tangent line is horizontal. Graph the curve and locate these points. Provide scales on both axes. Suggestion: On Desmos, let-2 st s 2 to see the full curve and to estimate where these points are. Points