-y-x4-y₁ #21 Given f(y)= (a) Find the direction in which f(cy) decreases most rapidly at P. (0,0), as well as the rate of change of fat Po (b) Find and classify all crit. points of f (c) Find the abs, minimum and abs.f maximum of f(x, y) on the triangle with vertices (0,0), (1,2) and (-1,2). Note 6x24x³-2=-2(x-1) (2x+1), -6x=4x+2=-2(x+1)(2x-1) and shade

Q: Where are the relative extrema (local maximum and minimum) on the curve? y = 3x² – x A. (0, 0) only…

A: given curve is y=3x2-x3 find the local maxima and local minima

Q: Find the directions of maximum and minimum change of f at the given point, and the values of the…

A:

Q: Find the curve in the xy-plane that has a slope at each point given by 1 and passes through the…

A: See attached file for a step by step explanation.

Q: y - 2)2 + (x-2)2 . Find the direction of heat flow in the plate at the point (2, 1). Heat flows in…

A: Introduction: The gradient of the temperature function at the point is the direction of the greatest…

Q: Consider the function f(x) = 4x − x² and the point P(1, 3) on the graph of f. (a) Graph fand the…

A:

Q: Parameterize the following portions of curves: (a) e The straight line between (-5, 3) and (11, 11).…

A:

Q: A circular disk of radius 5 meters centered at the origin has been unevenly heated. The temperature…

A: To find where the temperature on the disk is the greatest, we need to find the maximum value of the…

Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

A:

Q: (e) The instructor adds 4 points to the average exam score ofeveryone in the class. Describe the…

A:

Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: Find a simple closed curve Cwith counterclockwise orientation that maximizes the value of C3 4x: O…

A: Given ∮13y3dx+4x-13x3dy

Q: a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t,…

A: Given, a projectile launched at t = 0 second that follows a path x=30t, y=-5t^2+80t where x…

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

A:

Q: (2) Find all points on the graph y = x3 - 12x + 9 with horizontal tangents. Find dy d2y and dc d2…

A: Given:

Q: Find sin (2x)cos (2x)dx.

A: