1.) Investigate the function f(x) = 1 / (x2 - 1) according to the given plan:  a. Write the domain.  b. Find the derivative of the function.  c. Draw the sign diagram for the derivative and indicate on it the intervals of increase/decrease; find the minimum/maximum points.  d. This function has vertical and horizontal asymptotes. Write their equations. Using the information obtained, sketch the graph accordingly.

Q: If you are given the equation of a tangent function, how do you find a pair of consecutive…

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Q: 3. Find the equation of the tangent to the graph y = xvx-1 at ( 5, 10).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: The slope of the tangent line to the graph of the function y = 7V-3 at (9, 18) is

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Q: Find an equation for the tangent to the curve at the given point. y = (x^2)+2; (2,6)

A: Given:y=x2+2 (2,6)

Q: Do the graphs of the functionshave any horizontaltangent lines in the interval 0≤ x≤ 2p? If so,…

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Q: Find the equation of the line tangent to the graph of the function at the indicated po 4/5 y = (x² +…

A: Consider the given function as y=x2+2845

Q: 2. Consider the function h(x) = 11 - + x3 a) Find the equation of the tangent line to the graph of h…

A: We will find the equation of tangent line as shown below

Q: Find an equation of the tangent line to the graph of y=-8x/x^2+1 at the origin and at the point…

A: To find the slope of the tangent we find dy/dx We will use the quotient rule

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -4 and g' (6) = 3.…

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Q: If f(x) = 7x2 - x³, find f'(1) and use it to find an equation of the tangent line to the curve y =…

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Q: - 4x and draw the tangent lines to the graph at points whose x-coordinates are Graph the function…

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Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: Find an equation of the tangent line to the graph of the equation at the given point. y = 9-x2; P…

A: Solve for the equation of the tangent line

Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent.

A: Given that  f(x)=(-8x)/(√(2x-1))  The function has a horizontal tangent  To find the point at which…

Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

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Q: c) Finally, draw a large and clear sketch of the graph of f(x) = 2² – 2 and illustrate the tangent…

A: The point slope form y-f(x0)=f'(x0)(x-x0) is the standard equation for tangent line, where (x0,y0)…

Q: Find the equation of the tangent line to the graph of x4y16=1 at the point (81,1/3) and at the…

A: We use slope point form to equation of tangent line.

Q: Find an equation for the tangent to the curve at the given point. y=x2-x. (-3,12)

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Q: Determine the point(s) at which the graph of -8x f(x) = 2х- 1 has a horizontal tangent. (х, у) %3D

A: Solution - The derivative of a function is 0 at a point where the tangent is horizontal. Let us…

Q: Find an equation of the tangent line to the graph of  y = g(x) at x = 6 if g(6) = −2 and g'(6) = 5.…

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -4 andg' (6) = 3.…

A: Slope intercept form-  Y = mx + c  m = slope = g'(x) At x=6,  m= g'(6) =3 c= intercept on y axis…

Q: If g(x) = 2 − x3, find g'(0) and use it to find an equation of the tangent line to the curve y = 2 −…

A: g(x)=2-x3differentiate w.r.t xg'(x)=-3x2Put x=0g'(0)=-3(0)2 g'(0)=0at x=0g(0)=2-02⇒y=2.equation of…

Q: In the given equation as follows, determine whether the statement is true or false. If it is false,…

A: Given statement : If the graph of a function has three x-intercepts, then it must have at least two…

Q: At which x location on the graph of f(x) = -x² - 2x + 15 is the slope of the tangent 0?

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Q: Find the slope of a line tangent to the curve of the given equation at the given point. y = x2 - 3;…

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Q: 1 Find the two points on the curve y=- at which the tangents have as slope of -.

A: Given,            The curve y=1x at which the tangents have as slope of -12.To find : The two points…

Q: 1 5 Determine the equation of every tangent to the curve y = =x° - 10x that has a slope of 6

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Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: If g(x) =x4-2 find g'(1) and use it to find an equation of the tangent line to the curve y= x4-2  at…

A: Derivative: g(x)=x4-2 The eq of the tangent at (x1,y1) is y-y1=dgdx(x1,y1)(x-x1)

Q: Find an equation for the tangent line to the graph of the function F(x) = V3x2 + 9 at the point (3,…

A: To find the equation of tangent of given equation.

Q: Find the slope of the tangent to the graph of the given function at the indicated point. g(x) = 9x2…

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Q: Find an equation of the tangent line to the graph of the function f(x) = 2x² - 4x +5 at the point…

A: Given, f(x)=2x2-4x+5

Q: For the function, find the point(s) on the graph at which the tangent line has slope 2. 1 y=x²-3x²…

A: Given y=13x3-3x2+7x+16 & m=2To find point on the graph: Rules of differentiation: (1)…

Q: Find an equation of the curve whose tangent line has a slope ofƒ′(x) = x2/3,given that the point (1,…

A: Given: f'x=dydx=x23 For finding equation of curve, we will use variable separable method So,…

Q: If g(x) = 6 − x3, find g'(0) and use it to find an equation of the tangent line to the curve y = 6 −…

A: Given,

Q: Given the graph of the function f(x) below, estimate the slope of the tangent line to the curve at z…

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Q: Find the slope and an equation of the tangent line to the graph of the function f at the specified…

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Q: Consider the following equation and point. f(x) = 3x2 – 6, (-1, -3) Find an equation of the tangent…

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Q: If an equation of the tangent line to the curve y = f(x) at the point x=2 is y=4x-5, find f(2) and…

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Q: Find an equation of the tangent line to the graph at the given point. x2y2 − 9x2 − 4y2 = 0,…

A: Given that, x2y2 - 9x2 - 4y2 = 0 Points are :  (-4, 23) We have to find the tangant line to the…

Q: If f(x) = 8x2 - x3, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A: The given function is f(x)=8x2-x3

Q: c) Finally, draw a large and clear sketch of the graph of f(x) = z² – 2 and illustrate the tangent…

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Q: Find the slope m and an equation of the tangent line to the graph of the function f at the specified…

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Q: Determine the equation of the tangent to the graph of y = x³ - 3x² + x+ 3 at the point x = -1

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Q: Find an equation of the tangent line to the graph of y = x³ - 3x - 1 at the point (2, 1).

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Q: For what value or values of the constant k will the curve y = x3 + kx2 + 3x - 4 have exactly one…

A: Given curve is y=x3+kx2+3x-4. A curve have exactly one horizontal tangent  at x=a if f'a=0.…

Q: At which point(s) does the graph of  y= e((x3-2x2+3x)/(x)) have a horizontal tangent line?

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Q: Consider the following function. f(x) = x* + 4x3 + 11 (a) Make a sign diagram for the first…

A: We have to find the sign diagram for first derivative,  sign diagram for second derivative,  sketch…

Q: If f(x) =3x2 -x3 ,find f ' (1) and use it to find an equation of the tangent line to the curve y=…

A: Our Aim is to write an equation of tangent line to the curve y=3x2-x3 -(i) at the point (1,2).

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = 0 and B'(24) = -…

A: Given,         y=Bx at x=24 if B24=0 and B'24=-14.