The figure shows the graphs of f(x), f'(x), f"(x), and f"'"(x). Identify each curve and explain your reasoning: y a b

Q: Find the equation of the tangent line to the curve x' + y' = 6xy at (3,3). Write the equation in…

A: Given the curve x3+y3=6xy We need to find equation of the tangent line to the given curve at (3,3)…

Q: Find the points on the graph of y = tan x, 0sxs2n, where the tangent line is parallel to the line 4x…

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Q: At what points does the equation of the line tangent to the curve y=1/x have a slope equal to −1?

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Q: Please Find an equation of the line tangent to the curve defined by x^4+2xy+y^3=4 at the point (1,1)…

A: The given problem is solved below in detail.

Q: Does any tangent line to the curve y = 2x cross the x-axis at x = -1? If so, find an equation for…

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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 the slope of the tangent line to the curve - 2x2 + læy+ 3y = - 83 at the point (- 2, – 3).

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Q: Find the equation of the tangent line to the curve y = 5x² - 7 at a point x = 1.

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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: Find an equation of the tangent line to the curve x2y² – 2x = 9-y at the point (-2, 1)

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Q: Determine the family of curves such that at each point the slope is given by 2xy^2

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Q: Find the slope of the tangent line to the curve x² - xy - 2y³ 116 at the point (-2, 4).

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Q: Find an equation for the line perpendicular to the tangent line to the curve y = x3 - 4x + 1 at 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: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

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: On the same axes, plot the curve y = 1x, the line y = x/8, and the tangent line to y = 1x that is…

A: Given curve is y=x. Let x,y be any point on the curve. Differentiate function with respect to x.…

Q: What is the slope of the tangent line to the graph y = a° – 3x, | at the point (x1, Y1)?

A: Our Aim is to find the slope of the tangent line to the graph y=x3-3x -(i)at the point (x1,y1),

Q: Suppose a curve is defined by the equati on y2 = x*(2- x). What is the equation of the line tangent…

A: Given curve

Q: Find the equation of the tangent line.

A: Consider the given equation of curve:

Q: What is the slope of the line tangent to the curve defined by y +xy-x 11 at the point (2, 3)

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Q: Find the slope and the equation of the tangent line to the curve y=x²+1 at x=0. Sketch the graph

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Q: Find an equation of the line tangent to the curve defined by " + 5xy +y = 68 point (2, 2) at the

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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: at what point is the tangent line y3=2x2 perpendicular to the line x-y-1=0? P=(?,?)

A:

Q: Find an equation of the tangent line to the graph of y = 2x/x2+1 at the origin and at the point…

A: use differentiation for finding the slope and then use slope intercept form for finding the tangent…

Q: The equation of the tangent line to the curve 교+f -25, at (8,-12) is

A:

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

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Q: Find the equation of the tangent line to the curve y = 6x cos x at the point (7, The equation of…

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Q: Find an equation of the tangent line to the curve at the point (1, y = x4e-x

A: Given that      y = x4e-x We have to find an equation of the tangent line to the curve at the point…

Q: Find the equation of the tangent line to the curve y=(x-2) (x+1)? at point (3, 16).

A:

Q: Determine the equation of the line tangent to the graph given by y = at the point x +1 (4, }).

A: To find the equation of the line tangent to the graph y=xx+1 at the point 4,25

Q: Determine the equation of the slope of the line tangent to y = tan(x) using the 4-step rule.

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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: 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: At what point on the curve x = 9t2 + 7, y = - 5 does the tangent line have slope ?

A:

Q: Find the equation of the tangent to the curve y=x²-x -2 at the point (1, -2).

A: We have to find the equation of the tangent to the curve y=x2-x-2 at the point (1,-2).

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 equation of a tangent to the curve: y =. (x3 - 5x + 4)(3x2 - 2x) at the point (1,-2)

A: The given curve is y=x3-5x+43x2-2x at the point 1,-2.

Q: Find the slope of the line tangent to the curve y = sin' x at the point where x-x/3

A: We have to find the slope

Q: Please figure out the equation for the tangent line to the graph of the function at the point (9,…

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Q: Find the slope of the tangent line to the curve - 322 + 2xy – 3y° - 88 at the point (– 4, 2).

A: The given curve -3x2+2xy-3y3=-88 at the point (-4,2)

Q: Sketch the graph of y= x²+ - by using the properties of the derivative. 2

A: To sketch the graph

Q: Find the point(s) on the graph of y = (x2 - 143)eX where the tangent line is horizontal.

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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 equation of a line tangent to the graph: f(x) = xm) at xo = 1

A:

Q: At what point (x,y) is the tangent line to the curve y=2x2-5x+8 parallel to the line y=3x-7

A: It is given that

Q: Determine the equation of the tangent line to the graph of y = y2 – x² at the points (분 ) and (블, )

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Q: Estimate the slope of a line tangent to the curve f(x) = -2x2 + 3x +5 at point P(1, f(1))by doing…

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Q: Find an equation of the tangent line to the curve x2/3 + y2/3 point (1,8). 5 at the

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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: