Determine and sketch the contour plot for the function f (x, y) at three level curves.

Q: Find the equation of the tangent line to the graph of the function f (z) = (2² + 8) (z – 4) at the…

A: The solution are next step

Q: Determine the values of x where a curve y = x3 - 3x2 - 9x+ 12 has horizontal angent lines.

A: Given,         y=x3-3x2-9x+12

Q: The slope of the tangent line to the graph of the function y = 2/x – 6 at (36, 6) is 6 -0.50 0.17…

A:

Q: Write an expression for the slope of the tangent line to the  curve y − f(x) at the point (a,f(a)).

A: Given: The equation of curve is: y=fx Given point is a, fa.

Q: Draw a contour map of the function showing several level curves. f(x, y) = xy

A: To draw contour map of   f (x,y) = xy

Q: Find the equation of the tangent line to the graph of the function f (z) = (22 +9) (z – 3) at the…

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Q: Assume that y is a function of x. For the function (see attached), find the equation of the tangent…

A: We have to find dy/dx at (4,1)  We differentiate both sides with respect to x. Then plug x=4 and y=1…

Q: Explain how to find points on the curve x = f(t), y = g(t) at which there is a horizontal tangent…

A: Consider the following parametric curves. x=ft, y=gt Now, to find the tangent line at a point on…

Q: Let f(x, y) = 3x2 – xy+ 2y2. Then an equation for the tangent plane to the graph of f at the point…

A: Given f(x,y)=3x2-xy+2y2

Q: find the gradient of the function at the given point.Then sketch the gradient, together with the…

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Q: Graph the parabola f(x) = x2 . Explain why the secant lines between the points (-a, f(-a)) and (a,…

A: We have the given equation of parabola as fx=x2 On considering the solution set, which satisfy the…

Q: The slope of the curve f(x)= at x =1 is

A: given function :

Q: sketch the domain of f(x,y) = sqrt(x^2-y) and describe the level curve

A: Domain of a function is the collection of all values that go into a function. A level curve of a…

Q: Find equations of the two tangent lines to the graph of f that pass through the indicated point.

A: Given, f(x)=4x-x2…

Q: (iii) On your graph, draw a tangent to the curve, y = 2x +-10, that has a gradient of 1.

A: Given curve is y=2x+16x-10 Now, find the first derivative. y'=2-16x2-0y'=2-16x2 If the gradient is…

Q: Prove that the inflection points of y = sin x are at the x-intercepts.

A: Inflection points are points where concavity changes that is where double derivative is zero

Q: *(x, y) = xe"

A:

Q: Find a function f such that f'(x) = x“ and the line 2a - y = 3 is tangent to the graph of f. り

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Q: Let f(r, y) = - (5x² + 4xy+ y²). Then an implicit equation for the tangent plane to the graph of f…

A: Given function is, fx,y=−5x2+4xy+y2 To find the implicit equation of tangent plane to the graph of f…

Q: Find all points​ (x,y) on the graph of y=x/(x−1) with tangent lines perpendicular to the line y=x−8.

A: The given function for the tangent is, Differentiate the above expression to get the slope of the…

Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

Q: show that the sum of the x-intercept and y intercept of any tangent line to the curve x1/2+…

A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

Q: find an equation of the tangent plane at the given point. f (x, y) = x2 + y−2, (4, 1)

A: To find equation of tangent plane at (4,1)

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

A: Gradient problem....

Q: Determine the area of the triangle formed by the tangent to the graph of the function y=3−x2 drawn…

A:

Q: Show that the tangent line to the curve y = x3 at any point (a, a3) meets the curve again at a point…

A: Proof: The given curve is y=x3. Obtain the derivative of the function as follows: dydx=ddxx3…

Q: Consider the function  f(x) such that (a)  f(1)=10 and (b) the tangent line at  (x,f(x))  has slope…

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Q: Determine the values of x where a curve y=x³-3x²-9x+12 has horizontal tangent lines

A: Given,y=x3-3x2-9x+12differentiating both the sides w.r.t. xdydx=ddxx3-3x2-9x+12dydx=3x2-6x-9

Q: Find the equation of the tangent line to the curve y = f(x) at the given point. y = f(x) = x²-x, at…

A:

Q: Find all points (x, y) on the graph of y = x/(x - 2) with tangent lines perpendicular to the line y…

A: Given:

Q: Let (img) Use the fundamental calculus theorem to determine the slope of the tangent line to the…

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Q: %3D %3D .2 ,2.

A:

Q: Find all points (x, y) on the graph of y = with tangent lines perpendicular to the line y= 4x - 3.…

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Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: Find the x and y coordinates on the graph of f (x) = x³ - 3x where the tangent is horizontal. (A)…

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Q: Find an equation of the tangent plane to the graph z = Væ + y³ nt (8, 2, 4).

A: We know that equation of tangent plane to the graph z=f(x,y) at point (a,b,c) is…

Q: Use the guideline of this section to sketch the curve 1. y = 1 + 1/x + 1/(x ^ 2)

A: To Sketch: y=1+1x+1x2 Explanation: (a). Domain and Range y=1+1x+1x2is defined everywhere except…

Q: Find the equation of the tangent plane to f(x, y)= x´ – x y – y at point P (1, 1, -1).

A: Consider the equation

Q: Let y(x) = 2. x+2 Estimate the slope of the tangent line of y(x) at the point a = 0:

A: The given function is: y(x)=1x+2

Q: 1. Find the set of points in the curve y = A where the tangent lines are horizontal.

A: we have to find the set of points in the curve y=4xx2+1 where the tangent lines are horizontal. as…

Q: Sketch the line tangent to f at the point corresponding to x = -1. Label it as T.

A: d) The tangent to the given function at x=-1 is as given in the following figure.

Q: Find the distance between the point (1,1) and (3,9) along the curve y=x2

A: Given:The points (1,1) and (3,9) along the curve y=x2To find the distance we need use calculus as…

Q: Two different level curves of the graph of z = f(x, y) can intersect. True False

A:

Q: Use the graph to estimate the slope of the tangent line to y = x" at the given point. Verify your…

A: It is required to find the slope of tangent line from graph and then verify it analytically.

Q: Find all points (x, y) on the graph of y with tangent lines perpendicular to the line y = 4x - 5. (x…

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Q: Assume that f is a differentiable function where f(3) = 5 and f'(3) = 2. Find the equation of the…

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Q: Find the tangent to the curve a"-'y = x"

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Let y(x)=1/x+3 Estimate the slope of the tangent line of y(x) at the point x=1.

A: Given query is to find the slope of the tangent.