Using first principles, determine the equation of the tangent line at point (2,2) on the curve f ( x ) = x2 −7x+12.

Q: use the definition of a derivative and use it find and equation for the tangent line to y=2x2+2 when…

A: Equation of the tangent line: - We know that the equation of a line with slope 'm' that's passing…

Q: Find the equation of the tangent line to the graph of y?- x+1=0, at the point (2,-1). %3D

A: Here we havw to find the equation of the tangent line to the graph y2-x+1=0 at the point (2, -1)

Q: Use three-point midpoint formula to evaluate the first derivative of y = x² + 4x - 5 at x = 0 using…

A: Given function is y=x2+4x−5. We have to evaluate the first derivative of y=x2+4x−5 at x=0 using 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: Find the slope of the tangent line to the curve defined by x2 – 3xy – 3y = -84 at the point (-6, 4).…

A: To find the slope of the tangent line to the below curve the point (-6,4)

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: Using implicit differentiation, for the equation x³ + y³ = 9 is

A: Given: x3+y3=9

Q: Find the slope of the tangent line to the curve 3x? – 3xy – 2y = - 92 at the point (- 2, 4).

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Q: Find the slope-intercept form of the equation of the tangent line to the curve defined by x-2 3…

A: Equation of tangent line at the point (a,b) of the curve y=f(x) is f(x)-f(a)=f'(a)x-a

Q: Using the definition of derivative, show that f'(2) = for f (x) = Vx+ 2.

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Q: Find the equation of the tangent line to the graph f(x)=x^4 +2x^2 -x at x=1. Write your equation in…

A: Equation of tangent line to the curve fx at point x=a is given by y-fa=f'ax-a Given curve is…

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: 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: Q3:- Use the definition of derivative to find the tangent and normal equations of f(x) = x-3

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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: Find an equation of the tangent line to the curve y = 9^x at the point (2,81)

A: Given the curve is y=9^x at the point (2,81).

Q: Use the definition of derivative (do NOT use the short cut method) to find f'(x) given that f(x) =…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: 1. Find an equation of the tangent line to the curve y = 2x3 – 5 at the point (-1,3).

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 2x² 9 x2

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Q: Using the definition, calculate the derivative of the function = 2t3.

A: The given function is: s=2t3

Q: The tangent line to the curve y = x3 - 6x2 - 34x - 9 has slope 2 at two points on the curve. Find…

A: Given,  The tangent line to the curve y=x3-6x2-34x-9 has Slope=2 at two points on the curve.…

Q: 8. Use first principles to determine the derivative of each function. Then, determine an equation of…

A: Since multiple questions are asked in form of subparts a,b,c,d. Where in each part we need to…

Q: f(x) = x² + 2x when x

A: The answer is given below

Q: Find the equation of the tangent to the curve y = 2x2 - 5x + 3, where x = 2.

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Q: Find the slope of the tangent line to the graph y = x' - 3x +x at the point (2,–2). Hence, find the…

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Q: What is the equation of the tangent line to the curve at the point on the curve where x = - 2? (The…

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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: Find an equation of a tangent line to the curve y = 3x³72 + at the x2 point (1,5). Write you answer…

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Q: f(x) = √x2−2​ ; x = 2 what is its derivative?

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Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y =…

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Q: Write the equation of tangent line to the graph of y= x^2-9x/3x-x^3 at x= 3. Chex the reasonableness…

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Q: Using the definition of the slope of a tangent line, find the derivative of each function. 1. f(x) =…

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Q: Find an equation of the tangent line to the curve at the given point y = 2x3 - x2 + 5, (2, 17) y =

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Q: Using the definition of derivative, find the derivative of f(z) = x + 5x + 5. %3D

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Q: Q1. Find the derivative of f(x) = 2x² -- by using the definition of derivative.

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Q: How do you use Implicit differentiation find x^2+2xy−y^2+x=2 and to find an equation of the tangent…

A: The given equation is, x2+2xy-y2+x=2. Differentiate the given function with respect to x.…

Q: Find the equation of the tangent to the curve y = x/2x² + 7 at x = 3.

A: Topic = Application of Derivative

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: If (x) = 8x² - x, find f(1) and use it to find an equation of the tangent line to the curve y = 8x-…

A: First of all find derivative and slope

Q: Use implicit differentiation to find an equation of the line tangent to the curve 1 1 2x+3 2y-3 at…

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

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Q: How do you find the equation of the tangent line of the given value of x.

A: Calculation:Compute the value of f(x) at x = 4 as follows.f(4) = 2 − √4f(4) = 0.Now differentiate…

Q: Find the slope and equation of the tangent line to the curve y = x3 + 2x + 1 at ( 2,4)

A: Our Aim is to find the slope and equation of the tangent line to the curvey=x3+2x+1 at (2,4) -(i)

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: 8. Use first principles to determine the derivative of each function. Then, determine an equation of…

A: Equation of tangent is given by- y - y1 =  m (x - x1)

Q: Use implicit differentiation to find an equation of the tangent line to the curve 2-x +x-y+ 2·y² = 5…

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Q: How do I find the derivative of this problem?

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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…