Determine the concavity of the graphs of y^2=x and y=x^3

Q: Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from…

A: The line passes through the point (6,7) that cuts off the least area from the first quadrant.

Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

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Q: Determine the slope of the curve y =1/x+1 at point (−2,−1).

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Q: Find the equation of the line tangent to the graph of y = 2x - 8x2 + 2x -6 at x = 2. | %3D

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Q: draw 4 level curves of f(x,y)=e^-x+y

A: Given f(x,y)= e^(-x) +y The level curve are           e^(-x) + y = k    or.  y= k - e^(-x) Which is…

Q: Find an equation of the line tangent to the graph of y = exat x = 0.

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Q: There is a line through the origin that divides the region bounded by the parabola y = 7x X-axis…

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Q: Find the length of the curve y ' = 8x from x=1 to x = 8 www

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Q: How can we find Level Curves?

A: Level curves A level curve is simply a cross section of the graph of z=f(x,y) taken at a constant…

Q: Find distance between point A(1,3) Perpenclicular on the line L: 2y =2 +X

A: Use the following formula: The perpendicular distance from the point A(x1,y1) to the line ax+by+c=0…

Q: Describe the Chain Rule for the composition of two differentiable functions in your own words.

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Q: Find the shortest distance between the line y - x=1 and the curvex =y.

A: NOTE: Refresh your page if you can't see any equations. . the given line is  compare this…

Q: Find the equation of the line passing through the point (4,5) and perpendicular to the line y= x+2…

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Q: Find the point where the line tangent to y=x* – 3x² +2 at (2, 6) crosses the x – axis.

A: y=x4-3x2+2,  2, 6 Differentiating with respect to x, we get dydx=4x3-32x+0=4x3-6x Now slope of the…

Q: Find the slope and y-intercept of the line through the point (1,5) that cuts off the least area from…

A: In the question we have to find slope of line and y-intercept.

Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: Sketch a graph of y = 2 on [-1, 4] and use geometry to find theexact value of function given

A: Given : y=2 on -1,4 The graph is shown below: The shaded region is the required value of ∫-142dx

Q: Find the slope and y-intercept of the line through the point (10,9) that cuts off the least area…

A: Equation of line in point slope form : (y - a) = m*(x-b)  Where, slope = m and point = (a,b)

Q: Find the slope and y-intercept of the line through the point (4,10) that cuts off the least area…

A: We have to Find the slope and y-intercept.

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

A: Given, the curve y = ƒ(x) in the xy-plane that passes through thepoint (9, 4) and whose slope at…

Q: How do I know whether a graph is a vertical stretch, vertical compression, horizontal stretch, or…

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Q: at the line x = 3. %3D

A: Find the volume of the solid generated by revolving the region between the parabola  x=y2+1 and the…

Q: Find the coordinate of the local maximum for the curve 21 y=2+9x- +2x

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Q: Find the slope and y-intercept of the line through the point (6,6) that cuts off the least area from…

A: Given : Point (6,6)

Q: There is a line through the origin that divides the region bounded by the parabola v X-axis into two…

A: Given- There is a line through the origin that divides the region bounded by the parabola y = 7x -…

Q: use graphs to find approximate solutions ex = 4

A: we have to use the graph to find the approximate solution of ex=4.

Q: At whhat point on the parabola y = x - 3x-5 is the tangent line parallel to 3x-y 2

A: Given y=x2-3x-5 To find the tangent line parallel to 3x-y=2

Q: Differentiate the function. y = etan(8) y' =

A: The given function is y=etanθ.

Q: Find the equation of the line through the point (2, 5) that cuts off the least area from the first…

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Q: Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent…

A: We have to find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis…

Q: Sketch the curve y = x/(x² – 9). Enumerate the steps in your solution.

A: as per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – 3x and…

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Q: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

Q: Help 18 cubic function whose graph has horizontal tangents at (-2,6) and (2₁0). {Y= ax ³ + bx²²…

A: Let's solve.

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 2x and…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

Q: Find the point on the curve y = 3x + 4 which is closest to the point (5, 0). Preview Preview

A: Let (x, y) be the point closest to the point (5, 0) We will calculate the distance between these two…

Q: Sketch a graph of y = 2x on [-1, 2] and use geometry to find theexact value of function given

A: Let's sketch the graph of the following function:                                       y=2x…

Q: Find the equation of the family of curves whose slope at any point (x,y) is   2. x/y

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Q: Find the slope and y-intercept of the line through the point (2,7) that cuts off the least area from…

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Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: y 1-

A: The solution is given below in the next step:

Q: the shaded area shown in the figure is bounded by the line with equation y = 12-7x-x² and the line…

A: given functions are                                              y=12-7x-x2, y=4…

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

A: Given,            y = 3 - x2 , and the point 1, 2

Q: Find the slope and y-intercept of the line through the point (1,2) that cuts off the least area from…

A: Given : Point ( 1 , 2 )  It cuts off the least area from the first  quadrant

Q: Explain whether the Quotient Rule should be used to find the partial derivative

A: Partial Differentiation:     ∂∂x(xyx2+1)ddx(uv)=v.dudx-u.dvdxv2

Q: Find the area bounded by the curve 4 square units 8 square units 16 square units 10 square units =…

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