find all points (x,y) with x=y that are 12 units from (1,-5)
Find all of the points of the form (x, −x) which are 5 units from the origin.
(5 points) Find all 5 equilibria for the system of first order ODES dx = x(4-y-12) dt dy = y(x2-1) dt
#10 and #12
8. Find all points (.y) where fCx.y) -3x2 + 7xy -4y2 + x + y has possible relative maximum or minimum values 9. Find all points (x,y, z) where f(x,y,z) 5+ 8x 4y+x2+y2 z2has possible relativema imun or minimum value 10. Both first partial derivatives of f(x.y)-x-4xyy are zero at the points (0 11. Find all points (x,y) where f(e.y) 2x2+3xy + 5y has possible relative maximum or minimum values. Then, use the 12. Use the second...
1. (12 points) Find all the critical points of f(x) = (x - 1)(x + 5) Hint: Do not expand! Instead use the product and chain rules then factor 2. (12 points) Find the absolute extrema of f(x) = on (-1,2). Give your answers as (x,y) points. Hint: It is much easier to take the derivative of f(x) by rewriting as f(x) = (1 + x4)-1 and use the chain rule 3. f(x) = ? - 7x + 1 (a)...
Find all points on the x-axis 5 units away from the point (2, −4).
8. (12 pts.) Find all the relative extreme points of the function f(x,y) = y* – 32y + - x?.
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points off. (b) Classify each of the critical points; that is, what type are they? (c) For the same function f(x,y), find the maximum value of f on the unit square, 0 SX S1,0 <y s 1.
12. (5 points) (a): Find the directional derivative of f(x, y) = y² In r at P(1,4) in the direction of u = -3i + 3j. (b): Find the equation for the tangent plane and normal line to the surface cos(70) – z’y+e*2 + y2 = 4 at P(0,1,2).
for all points on the graph of y = 2cos x+5 where the slope of the 6. Find the values of x in OSx< tangent line is -1. (10 pt) be
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)