For the function f(x, y) = x² - 4xy + 4y² + 4x + 5y +4, find a unit tangent vector to the level curve at the point (4, -1) that has a positive x component. 4 Round your numbers to four decimal places.

Q: Find the tangent to the parabola (x + 2y)² + 2x - y - 3 = 0, parallel to the line x - y = 1.

A: Consider the equation of the line x-y=1 ⇒y=x -1 Comparing with y=mx+c we get slope of line, m=1

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A:

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope -12 at x = -1, and…

A: To find a parabola with equation.

Q: 2yy" = 1 + (y')² 2

A:

Q: Using implicit differentiation, for the equation r3+ y³ = 7 is y?

A: Solution is given as below:

Q: Plot the curve x³ + y3 = 6xy together with the tangent to the curve at the point

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Q: For the curve 2² - 4xy² = y³ +9, do the following:

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Q: Find values of a and c such that the tangent to y = ax2 + 12x + c is horizontal at the point (2,5)

A: Tangent is horizontal where derivative is zero

Q: Find the slope of the tangent line to the curve

A: Follow the procedure given below.

Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

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Q: x = t* + 2; y = t³ + t; find the equation for the tangent line at the point (2,0).

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