Locate the inflection points of the curve y = e²x²

Q: Find the equation of the tangent line to the curve at a given point  y=x3-3x+1 (3, 19)

A: Given,

Q: Use the guidelines of this section to sketch the curve.   y = x/ x-1

A: To find the x-intercept we plug y=0 So x-intercept is 0 To find the x-intercept we plug x=0 So…

Q: Find an equation of the tangent line to the curve at the given point. y = 4x – 3x, (2, –4)

A: Given, y=4x-3x2Point=2, -4

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

A:

Q: Find an equation of the tangent line to the curve: 4x^2 - 24xe^y + y = 13 @ the point (-1/2, 0).

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Q: Use the guidelines of this section to sketch the curve   y =x ln x

A: We can not have a negative number inside log, so x>0 This is the domain of the function.  We will…

Q: Find an equation of the tangent line and normal line to the curve at the given point. y = (2x)/(x2 +…

A: Given :          y=2xx2+1     1,1

Q: Find the point(s) on the graph y = x3 where the line through the point (4, 0) is tangent to y.

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Q: Locate the points of inflection of the curve y = (x^2)(e^x) * -2± /3

A: Solve the following

Q: Find the point on the curve y2 = ;(x+1) which is nearest the origin.

A: We have to find the point on the curve y2=52x+1 which is nearest the origin.

Q: (A) Find the equation of tangent and normal to the curve 2x2 + y = 9 at (-2, –1).

A: To find the equation of tangent and equation of normal at the given curve .

Q: (A) Find the equation of tangent and normal to the curve 2x+y² (-2,-1). = 9 at

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Q: Determine the parameter equation of the following curve x2 + y2= 5

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Q: Find an equation of the tangent line to the curve y= 10xat the point (1, 10).

A: Given: y=10x for finding tangent of given curve at given point we need slope m of tangent at given…

Q: Find an equation of the tangent line to the curve at the given point. y = 2x3 – x2 + 4, (2,16) y =

A:

Q: Determine slope of a curve y = x³ + 1 at x = 1

A: Given,           The slope of the curve y=x3+1  at x=1.

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

A:

Q: The equation of the tangent line to the curve y = x2 – 4x at the point where the curve crosses the…

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Q: Find the point on the curve y2 =(x+1) which is nearest the origin.

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Q: Find the equation of the tangent line to the curve at the given point. y = /2x +1, (4, 3)

A: To find the slope, we find dy/dx at (4, 3) At (4, 3):

Q: Find an equation of the tangent line to the curve at the given point

A: We have given the curve y = x5 + 3e5 and the point (0, 3). Find the slope at x = 0. Therefore, we…

Q: (B): Find an equation for the tangent and normal Line to the curve (y 2x +4x-3) at (x1)

A:

Q: I Discuss the properties of the curve and sketch fully: a) y = x? e-x

A: (a) Given- y=x2e-x To Find- The properties of the curve and sketch the curve.

Q: Determine slope of a curve y = x³3 + 1 at x = 1

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Q: Find an equation of the tangent line to the curve at the given point y = x³ – 3x + 1, (2,3)

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Q: Use the guidelines of this section to sketch the curve.   y= 3√(x2  -1)

A: We need to find the x intercept, y intercept, vertical asymptotes, horizontal asymptote etc to…

Q: Use the guidelines of this section to sketch the curve   y = x e -1/x

A: The given function is y=xe-1x. Sketch the graph of the above function as shown below.

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 and normal line at the point indicated. Sketch the curve. y = x –…

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Q: Use the guidelines of this section to sketch the curve.   y = 1/ x2 -9

A: Let us plot a table with values of x and y. x y 0 -8 1 -8 -1 -10 2 8.75

Q: Find an equation of the tangent line to the curve at the given point. y = sec(x), (7/6, 2/3/3)

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Q: Determine any critical points, point/s of inflection and trace the curve. y = x2(2 - x2)

A: Here we use concept of derivative

Q: What is the slope of the tangent line that touches the graph of In y + e2a-1 = 3y – 4x at the point…

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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: Find a point on the curve y = x2 that is closest to the point (18; 0)

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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: Determine the critical points of the curve y = x³ – 5x2 - 36 x + 25.

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Q: Find the x-coordinate of the point where the curve y = x3 - x crosses the horizontal line y = 1.

A: Given:                                 y=x3-x and y=1  Let                                y=x3-x…

Q: Parameterize the curve: x2+25y2-4x+100y+4=0

A:

Q: Find an equation of the tangent line to the graph of y=e^-8x at the point (5,e^-40)

A: To find an equation of the tangent line to the graph of y=e-8x at the point (5,e-40).

Q: Use the guidelines of this section to sketch the curve   y = x e -x

A: Consider the given function as y=xe-x

Q: Find the equation of the tangent line to the curve y=x-6cos(x) at the point (0,-6)

A: We have to find equation of tangent line to the curve y=x-6cos(x) at the point (0,-6)  Now first we…

Q: Find an equation of the tangent line to the curve at the given point y = x3 - 2x + 2, (2,6) y =

A: From the given data:

Q: Find the slope of the curve, equations of the tangent and normal lines to the given point. y = x3 –…

A: We have to solve the problem

Q: Find an equation of the tangent line and normal line to the curve at the given point. y = x* – 2e*,…

A: Given curve is y=x4-2ex. To find the equation of the tangent line and normal line to the curve at…

Q: a) y = x? e-X

A: We have to discuss properties of the graph