#8, Given f(xy)=3x4-2x³y. (a) Find the rate of change of f in the direction of vector u=(-1,47, it the point Po (-1,-2). (b) Find the linearization L(x,y) near Po and use it to estimate f (-0.96,-2.03) (c) Find an upper bound for the error incurred in replacing by L on the rectangular region -1.04≤x≤-0.96 R: -2.03≤ y ≤ -1.97 FL,

Q: (x)=3x-2√x I the equation of the secant line through the points (4,f(4)) and (9, f(9)). w that there…

A:

Q: Find the directional derivative of the function at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

Q: Use implicit differentiation to help you find the value of the gradient for the equation x² – ev =…

A: given equation x2-ey=yx-2+8 claim- use implicit differentiation to help you find the 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: Find the linear approximation to the function f(x, y) = sin y --- |T at x, = (1, -2) 2 and use it to…

A: The solution is given as

Q: The graph of y = f(x) has a y – intercept of 3 and the tangent line at the point (x, y) has a x-…

A:

Q: For the functions below, what is the direction of fastest increase at  (1, 1, 1)? (a) f(x,y,z) =…

A: The direction of fastest increase for a function at a point is the direction of the gradient of that…

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: The derivative of ƒ(x, y) at P0(1, 2) in the direction of i + j is 2sqrt(2) and in the direction of…

A:

Q: Find an equation of the curve in the xy-plane that passes through the point (2, 3) and has, at every…

A: integration

Q: Find the directional derivative of the function at the point P in the direction of the point . f(x,…

A:

Q: find the directional derivative for z=2xy-3sqrt(xy) at point (1,1) in the direction of point (3,2).…

A: Directional derivative is same as rate of change in that direction