Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an answer does not exist, enter DNE.) r = 2 + 3 sin() (-1,3 (2, 1) +0 2 3 dy dx = at (-1, 37) dy dx at (2,7) dy dx at (5,5) dy dx
parta-
Use linear approximation, i.e. the tangent line, to
approximate as follows:Let f(x) = x 6.
The equation of the tangent line to f(x) at x = 2 can be written
in the form y = mx+b
where
is:
and where
is:
Using this, we find our approximation for 1.86is
Box 1: Enter your answer as a number (like 5, -3, 2.2) or as a
calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity
Box...
3. Use implicit differentiation to find dy/da where 4x® - 7x*y2 = 3y - 6. Find the equation of the tangent line at the point (1, -1)
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
9. Here is a graph of the relation xy - y2 = 6. a) Confirm that the point (5,2) is in the relation. 5 [2 pts] -5 0 5 > -5 b) Find the slope of the tangent line through (5,2) Use methods of Calculus - do not just estimate. [ 5 pts)
(1 point) The graph of the equation 2? + ry + y2 = 3 is an ellipse lying obliquely in the plane, as illustrated in the figure below. a. Computer aligne = (-2x+y)(x+2y) . . b. The ellipse has two horizontal tangents. Find an equation of the upper one. The upper horizontal tangent line is defined by the equation y= c. The ellipse has two vertical tangents. Find an equation of the rightmost one. The rightmost vertical tangent line is...
16. Find all points on the circle x2 + y2 = 676 where the slope is 5/12 (x, y) = _______ (smaller y-value) (x, y) = _______ (larger y-value) 13.Find an equation of the tangent line to the graph at the given point. x2y2 - 9x2 - 4y2 = 0, (-4, -2√3) y = _______ 12. Find the slope of the tangent line to the graph at the given point. (4 - x)y2 = x3, (2, 2)
-7 -6 -5 4 A Find the slope of each line in the graph above. Give your answers as integers or reduced fractions. If a line does not have a slope, enter DNE. Purple Line: slope = Preview Blue Line: slope = Preview Preview Red Line: slope = Orange Line: slope = Green Line: slope = Preview Preview
Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.) y = 2x - In x (x, y) = _______ Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE. concave upward concave downward
Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)f(x, y) = y2 − 4y cos(x), −1 ≤ x ≤ 7local maximum value(s) DNE local minimum value(s) −16 saddle point(s) (x, y, f) = (π2,0,0),(3π2,0,0)