In Exercises 31-34, find the slope of the tangent line to the graph of the given function at the given value of x. Find the equation of the tangent line in Exercises 31 and 32. 32. y = -3x - &r + 4x; x = 1

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

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Q: Define the term derivative of a function at a point?

A: The derivative of a function f(x) is the rate of change of f(x) with respect to x. The derivative…

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 81x2…

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Q: Find equations of the tangent line and normal line to the curve  y= x sqrt x  at the point  (1,1) .…

A: Given curve: Let the slope of the tangent line to the given curve is m. And the slope of the normal…

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Q: Use the definition of the derivative to find the slope m of the tangent line to the graph of the…

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Q: The slope of the tangent line to the curve y=2x^3 at the point (-4,-128) is ____. The equation of…

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Q: Solve with solution determine the slope of the tangent line to the curve y=3x2 – 2x at the point…

A: Topic = Derivative

Q: Find the equation of the tangent line to the curve y = (2? - 8)' at point (5, 2). y =

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: The Gateway Arch in Saint Louis is modeled by the curve: y = 210 − 20 cosh ( x/30) . At what height…

A: yx = Height of the Gateway archyx = 210 - 20coshx30         Blue curve---------------------formulae…

Q: 4. What is the slope when you illustrate tangent line to the graph of the equation y 2x2 – 3x + 5 at…

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Q: Find equations of the two tangent lines to the graph of f(x) = 2x² that pass through the point (1,…

A: Given:- f(x) = 2x2  To find:- Equation of tangent lines passes through (1, -6)

Q: Find the slope and equation of the tangent line to the graph of the equation at a given point. 1. y…

A: Given y = 2x² + 4x.     Point ( -2 , 0 ) To find slope & equation of tangent line.

Q: . Find the slope and equation of the tangent line to the graph of the equation at a given point. 1.…

A: Topic:- derivatives

Q: Estimate the slope of the tangent line to the curve at the given point (x,y). 6- 4- (-2,2) -6. -4 -2…

A: Given figure,

Q: Find an equation for the tangent line to y = g(x) at the point (2, g(2)). Write your result in…

A: From graph we have g(2)=4 and therefore we compute the tangent of the graph y=g(x) at the point…

Q: Explain how you would approximate the slope of the tangent at a point without using first…

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Q: Explain how to find the tangent line and normal line equation when the slope is undefined?

A: It is given slope at the point is undefined say the point is (x1, y1).  The equation of tangent at…

Q: Find the slope of the tangent line to the graph at the given point. (x2 + 4)y = 8, (-2, 1)

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Q: 7. Find the equation of the tangent line to the curve y = - 1-3x at x =-1 using calculus and…

A: Given curve is y=21-3x At x=-1, y=21-3·-1=21+3=24=12 So, the point is -1,12

Q: Find the slope the tangent to the curve y² = 3x² + 4 through point (-2, -4)

A: Given: y2=3x2+4   , -2,-4

Q: What is the slope of the tangent line to the graph of y x*-3x +x +2 at x-2? What is the y-coordinate…

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Q: Find an equation of the tangent line to the graph of the equation: x+y-ex-y=5 at the point (3,3)

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Q: How many tangent lines to the curve y = x/(x + 1) pass through the point (1, 2)? At which points do…

A: The tangent lines to the curve y=xx+1 passes through the point (1, 2)

Q: Describe how to find the slope of the tangent line to the graph of a function at a point.

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Q: 4. at the point 8, The slope of the tangent line to the curve y is: - The equation of this tangent…

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Q: Draw the graph x2+y2=8, and the tangent line at (√3, √5), please write the equation for tangent line

A: Tangent equation.

Q: The slope of the tangent line equation to the graph of the function y = 5/x-9 at (81,36) i

A: Given:y=5x-9  at 81,36Equation of tangent line:y-y1=mx-x1

Q: What is the slope-intercept form of the equation of the tangent line to y=x²+2x at x=0?

A: At x = 0, y = 0+0 =0  So, the tangent line passes through (0,0) .

Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (-1,…

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Q: 11. What is the slope of the tangent line to the curve y = 3x2 - 5 at point (-1,-2)? а. -5 b. -6…

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Q: alculate the length of the tangent line, normal line, sub-tangent and subnormal from: a. x²+ 2² - 4x…

A: This is a problem related to derivative. Based on the general formula and concept we will answer the…

Q: Does the graph of -1, x0 have a vertical tangent line at the origin? Give reasons for your answer.

A: Given function is fx=-1, x<0   0, x=0   1, x>0.

Q: 3) What is the slope of the tangent line to the graph of y=(x-1)/(x+1) at x=0? Please answer this…

A: topic- slope of tangent line

Q: tangent line of the curve

A: The tangent line is the line on the curve which passes through the given point on the curve.

Q: Find an equation of the tangent to the curve at the given point. y = -2 In(x? – 3), (-2,0)

A: Given the point. Using point slope formula.

Q: Find an equation of the tangent line to the graph at the given point.  square root of x + square…

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Q: Find the equation of the tangent and normal line of the function f(x) = \sqrt(2x−1)​ at the point…

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Q: What is the slope of the tangent line to the graph of the solution of y'= 7√y + 3x³ that passes…

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Q: Illustrate the Derivative of Cosecant Function ?

A: Illustrate the Derivative of the Cosecant Function?

Q: What is the value of the slope of the tangent line to the curve y = 2x2 + x – 3 at the point…

A: Given :-  y = 2x2+x-3 To find:- slope of tangent line at (-1, -2)  METHOD:- Slope of tangent =dy/dx

Q: What is the equation of the tangent line of the function y = 2 + x² at point (3, -2)?

A: y=2+x2

Q: Find the equation of the tangent line to the curve y = x³ – 4x + 3 at the point (3, 18). Tangent…

A: Answer and explanation is given below...

Q: Find an equation of the tangent line to the curve at the given point. y = 7x2 - x3, (1, 6) y =…

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Q: What is the value of the slope of the tangent line to the curve y = 2x² + x – 3 at the point (–1,…

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Q: The tangent line equation of x++y“=32 at point (2,-2) is... Persamaan garis singgung kurva x++y*=32…

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Q: Find the slope and equation of the tangent line to the curve y = x2 – 4x + 5 at (2,-3)

A: Given curve is : y = x2-4x+5 We have to find slope and equation of tangent line to given curve at…