Sketch the curve: f(x) = x* – 6x²

Q: Use the guidelines of this section to sketch the curve   y =  x - 3x 1/3

A: Let us make a table for the function x -8 -1 0 1 8 y -2 2 0 -2 2

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: In the open interval 0, find the point where the slope of the curve y =tanx is 4?

A: in the open interval 0,π2, we have to find the point where the slope of the curve y=tanx is 4. the…

Q: Sketch the curve f(x) = x/(x-1)^2. Show complete solution

A: We have to sketch the given curve f(x) = x/(x-1)2. To sktech the given curve we will follow the…

Q: For the curve y = x² - 2lnx, locate all critical points and points of inflection.

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Q: Use the guidelines to sketch the curve  y = 2 x2  / ( x 2  -1 )

A: For, x=0, y=0  So, the y-intercept is 0   Then we plug y=0 and find x so, x-intercept is 0.

Q: Use the guidelines of this section to sketch the curve   y =x/  sqrt( x2   +1)

A: This function can not have the denominator equal to 0, so there will be no vertical asymptote.

Q: Does the curve y = x4 - 2x2 + 2 have any horizontal tangents? If so, where?

A: Consider the given function y=x4-2x2+2.

Q: Find the exact length of the curve. 글 cosh(2x), sxs8 y = 4 +

A: Given:

Q: Use the guidelines of this section to sketch the curve.   y = 2√ x    -x

A: We will make a table for the function  x 0 1 4 9 y 0 1 0 -3

Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ < t < ∞.

A: Given: x=3+2t y=-12-6t            - ∞ < t < ∞ To find: curve generated by given functions.

Q: Identify and sketch the curve for x2-y2-6x = 0

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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 equation of the tan gent line to the curve f(x) = /16–4x at (3,2) a)

A: To Determine: a. Find the equation tangent line to the curve

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

A:

Q: Find the point on the curve y = sqrt x that is closest to thepoint (3,0)

A: Given curve y=x Let A(x,y)  be a point on the curve and let B(3, 0) So distance between A and B is…

Q: 5. In y = x2 -5 at (V5, 1)

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Q: Use the guidelines of this section to sketch the curve.   y = (4 - x2)5

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Q: Write the equation of the tangent line to the curve (a lemniscate) 2(x2 + y²)“ = 25(x² – y²) at the…

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Q: What is the length of the curve y = sqrt(4-x2) from x = -2 to x = 1?

A: y=4-x2 Differentiating with respect to x, we get dydx=124-x2·d4-x2dx   ∵dxdx=12x=124-x2·0-2x=-x4-x2

Q: Use the guidelines of this section to sketch the curve   y =2 sqrt x - x

A: Given              y=2x-x

Q: write the equati on of the tangent and normal line line of the curve. huow your soution 2 2 4. f CX)…

A: Given: fx=x3-3x+4 at 2,6

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

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Q: Find a possible point of inflection of the curve y x +3x2 + 6x

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

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Q: Use the guidelines of this section to sketch the curve.   y = 2 + 3x2 - x3

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Q: Use the guidelines of this section to sketch the curve. х — 6 y = x2

A:

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: write the equation of the tangent and normal line line of the curve. huow soution your 2. (3.0) f…

A: First, check if the given point lies on the curve, f(x) . If the point is on the curve, then compute…

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: 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: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

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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)

A:

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: Sketch the curves 1.) y = 3+4x-x2

A: the equation of the curve is: y=3+4x-x2 we have to sketch the given curve.

Q: Find the length of the curve : y = + from x = 1 to x = 3 - 3 4x

A:

Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

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

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: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: write the equation of the tangent and normal line line of the curve. huow somtion your 1 . f(x) = -…

A:

Q: Identify and sketch the curve for: x2-y2-6x=0

A: Combine the like terms of x and y in the given equation, and then add 9 on both sides of the…

Q: Use the guidelines of this section to sketch the curve. y = x/7 - x2

A:

Q: nsider the curve x3 + y2 - 4xy = -2

A:

Q: Use the guidelines to sketch the curve; y= x/sqrt x^2+1

A: To sketch the curve y=xx2+1

Q: Locate the inflection points of the curve y = e²x²

A: The given curve is y=e2x2. The first derivative of y=e2x2 is, y'=ddxe2x2=2xe2 The second derivative…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: