Suppose that z is a difierentiable function of x and y with
If
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- 8. Find the directional derivative of f at the p in the direction of v= ( of f(x, y, z)=x²exx, p = (1,1,1) f(x, y, z) = sin(xyz), p = (1,1,1) 1) 2)arrow_forwardShow that the function given by f (x, y) = x² + 3xy is differentiable at every point in the plane. By using the definition.arrow_forward1. A function of two variables is given f(x, y) = x² + y² + e-(x²+y²) a) Draw a picture of the graph of the function f. Use for example Geogebra. b) Find a tangent plane to the graph of the function f at all points (x, y, f(x, y)) c) At what points is the tangent plane parallel to the xy-plane? How does the function behave near the points (0, 0)?arrow_forward
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- Suppose that f(æ, y) and at the point (x, y) = ( – 5, – 3) is xy. The directional derivative of f(x, y) in the directional | |arrow_forwardFind the directional derivative of f at the given point in the direction indicated by the angle 0. f(x,y)=√xy, (1,3), 0 = π/6 a. b. C. d. e. 1/1 (3+√³) 4 1/2 (3+√3) 1²/ (√ 3 + √²³) 3 — (3+√3) 4 √3 + (₁-4) 3 4 3arrow_forwardA function z=f(x, y) is defined implicitly by the equation xy2 - x²z+yz² -z = 11 near point (2, -2, -1). The directional derivative of this function in the direction of v = (4, 3) is a) 17/5 b) 7/5 O c) 11/5 O d) 31/5 e) 17/5 Of) 23/5 202arrow_forward
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