3. (10 points) Find the equation of the tangent line to the curve x² + xy + y2 = 3 at the point (1,1).
Consider the curve defined by the equation x² + xy + y2=4. The equation of the tangent line to the curve at the point (-2,2) is (show work)
Consider the curve to x? + xy + y2 = 4. defined by the equation The equation of the tangent line at the point (-2,2) is the curve
2. Find the equation of the tangent line to the ellipse z? - zy+y2 = 3 at the point (-1,1). Express your answer in slope-intercept form (y = mz+b).
at the point (2,1) Find an equation for the tangent line to the curve 22 - xy - y2 - 1 at the point
2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction 2. Find the slope of the tangent line to f(x, y) 6-x2 + xy - y2 at (4, 2), toward the point (7, 1). Then find the maximum slope and its direction
6. Find the equation of the tangent line at the given point. (a) x2 + y2 = 25,(-3, 4) (b) 2y - Vt = 4,(16, 2) (c) y + xy² + 1 = x + 2yº, x = 2
1. a) Find the equation of the normal line to the curve b) Find h’(3), if h(x) = 1. a) Find the equation of the normal line to the curve y = 5x3 - 2x2 +4 when x=2. b) Find hʼ(3), if h(x) x2 + 8e2x+1 X-1
Find an equation of the line tangent to the curve at the point corresponding to the given value of t. 71 x= cost+t sint, y=sint-tcost;t=4 (Type an equation. Simplify your answer. Type your answer in slope-intercept form. Type an exact answer. Use integers or fractions for any numbers in the equation.)
4. Find the equation of the tangent line to curve 3 (x2 + y2) ? = 25 (x2 - y2),= 1 at (2,1).