How fast does the  slope of the curve y= (x2+x+1)2 change at the point where x=2

Q: -1 What is the slope of the line tangent to the graph of y at x = -2?

A: Find the derivative of y to obtain the tangent as shown below: y'=ddxtan-1xy'=1x2+1

Q: 2x +1 Find the slope of the line tangent to the graph of y = 5x at x = 1. 4

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Q: 2. Find the slope of the tangent line to the curve y = 4x² – 2 at x= 1. What is the equation of the…

A: The given curve is y=4x2-2. At x=1, y=412-2=2. Thus, the graph is passing through 1, 2. The slope of…

Q: The slope of the curve y=ax3-bx2-cx-3 at x=2 is 5. If the point of inflection of the curve is at…

A: The slope of the curve y=ax3-bx2-cx-3 at x=2 is 5. If the point of inflection of the curve is at…

Q: Find the slope and equation of the line tangent to f (x) = x² – 4 at the point (3, 5).

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Q: 3. Find the tangent lines and normal lines to the curve y = x4 - 4x3 + 6x2 – 4x + 3 with slope…

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Q: The slope of a tangent to the curve f(x) = x² + 2x – 5 at the point (3, 10) is : 12 8. -5 10

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Q: Find an equation of the curve that passes through the point (0, 2) and whose slope is xy?

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Q: 1) What is the slope of the graph y = 5e³x at x = 1?

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Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of y/x2 at any…

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Q: the slope of the curve 2y2=ax2+b at (1,-1) is -1.find a,b

A: The equation of the curve is  2y2 = ax2+b…

Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: y=11-x Also, the given Slope is -1

Q: The curve for which y'' = 6 has a slope of –3 at its point of inflection (2, 3). Find the value of y…

A: y''' = 6 Implies, y" = 6x + a, where, a is a constant. &, y' = 3x² + ax + b, where, b is a…

Q: 4) Find an equation of the line tangent to the graph of 2x³y³ = 2y – 4x at the point (-1, –1). Show…

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Q: 2. (6 marks) Find the slope of the line tangent to f: y = 2/5x + 1 at the point (3,8). c) - D) E) -…

A: Answer and explanation is given below..

Q: Find the slope of the curve x2 + y3 = 2 at each point wherey = 1

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Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 3 the point (2, 2.8).

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Q: 3. Find the slope of the graph tangent to the curve y =x* - 2x3 +x that passes through the point (2,…

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Q: Find the slope of the curve x²+y²-6x+10y÷5=0 at point (1, 0)

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Q: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

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Q: 2. Find the slope of the curve at the point indicated. a. y = 5x – 3x²,x = 1 x-1 b. y =,x = 0 x+1

A: Find the slope

Q: 20. What is the instantaneous slope of y at x = 2? %3D -1 1 112

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Q: What is the slope of the line tangent to the curve x2 + y2 = 1 and parallel to the x-axis ? OA…

A: what is the slope of the line tangent to the curve x2+y2=1 and parallel to the x axis

Q: 25.For which x – values does the graph of y = e3x³-2x-4x have a horizontal tangent line ?

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Q: 2) Find the equation of the curve whose slope at any point p(x,y) is m =x (x +5)² and passing…

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Q: 1. What is the instantaneous slope of y = 5 at x = 5?

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Q: find the slope of the curve at the given points (x2 + y2)2 = (x - y)2 at (1, 0) and (1, -1)

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Q: Find the slope of the curve at the given point: 1. ( X+2y)^2 =x+10 at (-1, 2)

A: Here I am attaching image so that you understand each and every step. slope of the curve given at…

Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

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Q: Q4\ Find the slope of the function F(x) = √√x+1 at the point (8,3) And find the equation of the…

A: To find the slope of the function at the given point and also the equation of the tangent line at…

Q: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: What is the approximate slope of the curve with equation f(x)=(1/x-1) at x = 1.2?

A: To find the approximate slope of the curve with equation f(x)=(1/x-1) at x = 1.2

Q: The line y=3x+6 is tangent to the graph of y = (-48)/(x-6) at the point ?

A: The given equation of tangent is y=3x+6 and its tangent to graph of y=-48x-6. To find the points at…

Q: The slope of the curve y=x' +3x² – 6x +5 at (1,3) is -

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Q: 7. Find an equation of the line tangent to the curve y = 3x² – 1 and perpendicular to the line x

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Q: 01:- Find the slope of the curve f(x) = Vx – 1 at the point (x=5).

A: Topic-application of derivatives

Q: 3. Find the slope of the curve of the function y = at the point P (2,-).

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Q: Find the slope of the curve at the given point. y3= x3/2a-x   at (a,a)

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Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

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Q: 9. Find an equation of the line tangent to the curve y = 2x - 7x2 + 10 at the point (3, 1). y = 12

A: Given that, the curve is y = 2x2 - 7x2 + 10  To find the tangent line to curve at point (3,1)   To…

Q: a) Find the slope of the tangent to the curve y = 3+ 4x2 – 2x³ at the point where x = a.

A: We are suppose to solve the problem by application of derivative.   NOTE :: As per our guidelines we…

Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: 14. Find the slope of the curve y = 2x3 – 3x at (-1 , 1)

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Q: 4. Find the equation of a curve whose slope at any point is equal to x + + and which passes through…

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Q: Q2/ Find the slope of the tangent to the curve at x = 8 4 + पड़े + y = 3x5 + 2³√x+2+√5 X-Y 3x²

A: We know that slope (m) of the tangent to the curve y=f(x) is :  m=dydx We have y=3x5+2x3+13x2+5

Q: 49. Find the slope of the curve y = (2x2 - x+ 3)(x + x+1) at (1, 12).

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Q: 2а3x at (a, a) ,2 x2+a²

A: Given curve is,

Q: Find the equation of the family of curve whose slope at any point (x,y) is 3x^2+4

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Q: Two is the slope of the curve y = 4x + x2 at what point?

A: Slope of a curve is given by m=dydx  Use this formula to solve above question.

Q: 4) Find the slope of the curve y = 3x + 1 at point P (1,2)

A: We need to find slope of curve at given point.