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
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.
Find dy/dx. Find the points on the curve where the tangent is horizontal or vertical. x = t3 - 3t, y = t2 - 6
[8 points) For the curve given by x = t4 – t, y = Int + t2, find the equation of the tangent line to the curve at the point (0,1).
6. Let a curve be parameterized by x = t3 – 9t, y=t+3 for 1 st < 2. Find the xy coordinates of the points of horizontal tangency and vertical tangency.
1a) Find dy/dx x = te', y = t + sin t b) Find dy/dx and d’y/dx2 for which t is curve concave upward x = x3 + 1, y = t - c)Find the points on the curve where the tangent is horizontal or vertical. Draw the graph x = 13 – 3t, y = t3 – 312 d) Find the area enclosed by the x-axis and the curve x = t3 + 1, y = 2t – t?....
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
The curve Cis given parametrically by x = t2, y = y(t), and intere'. Find the interval of t where curve C concaves upward. o(-00,00) (0,1) (0,0) o(-0,0)