Find the slope of the tangent line at point (-2,2) on the curve f(x) = 2 x2 + 3x using First Principles.

Q: Find the equation of the tangent and normal line of the function f(x) = 2x – 1 at the point (5, 3).

A: fx=2x-1   First find equation of tangent line of given function  We need to find the slope of…

Q: Find the slope of the tangent line to the curve 4x2 – 2xy – y = 32 at the point (2, – 2).

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Q: Find the slope of the tangent line to the curve (a lemniscate) 2 (x + y ²)² = 25 (x² – y²) at the…

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Q: Find an equation of the tangent line at the point indicated. f(x) = 5x2- 2x,    X = 1

A: Solution:Given   f(x)=5x2-2x       x=1To find the equation of the tangent lineFormula:Equation of…

Q: What is the equation of the tangent line of f(x) = In(2x – 3) at the point x = 2?

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Q: Find the equation of the tangent line to the curve g(x) = 5x2 - 6x +2 at the point (1, 1).

A: Use equation of  tangent line

Q: Find the slope of the tangent line of f(x)=10x2-3 at x=-2.

A: Given f(x)=10x2-3and x=-2

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: 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 the slope of the tangent line to the curve of y = x 2 at the point where x = −6

A: Slope of the tangent line is the derivative of the given curve at the given point. So…

Q: Find equation of tangent y=x³-4x+1 at point (2,1)

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Q: Find the slope of the tangent line to the curve x² + 3xy + 3y³ = − 101 at the point (4, -3).

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Q: Find the slope of the tangent line to the curve - 4x² + 4xy - 1y³ = - 148 at the point (3, 4).

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Q: Find the equation of the tangent line  x2y-y3 + 6x= 8  at the (3, -2)

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Q: Find the equation of the tangent line to the curve 3x f (x): at the point (1,). 1+5x2

A: Given: The function fx=3x1+5x2 and the point 1,12, To determine: The equation of tangent line to the…

Q: Find an equation of the tangent line to the curve  y = x sq root of x  that is parallel to the line…

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Q: Determine the equation of the tangent line and the normal line to the curve f(x)=x3 -3x2 +2x +2 at…

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Q: Find the slope of the tangent line to the curve 4x2 + 2xy - 2y³ = 160 at the point (4, - 4). -

A: We have to find slope of tangent line to the curve  at the point (4, -4) that is dy/dx at (4, -4)

Q: 3. Find the equation of the tangent line to the curve f (x)= (1+2x)'" at the point (0,1) in…

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Q: Find the equation of the tangent line.

A: Consider the given equation of curve:

Q: 7. Find the slope of the tangent line at point (-2,2) on the curve f(x) = 2x² + 3x using First…

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Q: find the equation of the tangent line to the curve  8x2y3-5x2+7y3 = 10(x-3y) , at point (2,-2)

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Q: Find equation of the tangent line to the graph of y=sqrt(x^3-2) At the point where x=3

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Q: What is the slope of the tangent line to the graph of f(x) = x² - 3x +1 at the point (-1,5)?

A: Given: fx=x2-3x+1 To Find: The slope of the tangent line to the graph of the given function at the…

Q: Find the slope of the tangent line to the curve - 4x2 - 4xy + 3y³ = 204 at the point (- 3, 4). |

A: Basic application of derivative problem

Q: Find an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: Find the slope of the tangent line to the curve -x^2+2xy+2y^3=-10 at the point (-4,-1).

A: Slope of tangent line = dy/dx at the point (-4,-1)

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + 1y - 38 at the point (1, – 3). -

A: Where we use the concept of implicit differentiation then we evaluate the differentiation at the…

Q: Determine the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (√2, −1/√2).

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Q: The slope of the tangent line to the curve x^3 + y^3 = 6xy at the point (3,3) is

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Q: Find an equation of the tangent line to f(x)=-x – 4x at the point (-1,5).

A: The above question is answered in next step and we can find the equation of the tangent line

Q: Find the slope of the tangent line to the curve defined by 9x^2+7xy-4y^3=432 at the point (-9,3).

A: We have given the curve Here, the equation has to be differentiated implicitly.

Q: Find the point f(x)= x3 - 3x2 + x + 4 where the tangent line has slope 10

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Q: Find the slope of the tangent line to the curve -2x^2-3xy-3y^3 = -246 at the point ` ( 3,4 )`.

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Q: Find the slope of the tangent line to the curve 2² – -1 4.xy + 4y: at the point (1, - 1),

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Q: Find the slope of the tangent line to the curve - 3x² – 3xy - 4y³ = 265 at the point (1,4).

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Q: Find the equation of the tangent line on the curve f(x) = V5x + 6 at x = 2.

A: Proceed as shown below...

Q: Find the slope of the tangent line to the curve - 2x2 + 2xy – 4y³ = 0 at the point (1, – 1). -

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Q: Find the slope of the tangent line to f(x) = √9x³ at the point x = 4.

A: We have to find the slope of the tangent line to f(x)=9x3 at the point x=4.

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

A: The equation of the line passing through the point (x1,y1) having slope m is given as (y-y1)…

Q: Find the equation of the tangent and normal line of the function f(x) =√(2x − 1) at the point (5,…

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Q: Find the slope of the tangent line to the curve - 2x² - 2xy - 1y³: 1y³ = - 11 at the point (-2,-1).

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Q: Find the slope of the tangent line of f (x) = 2x² - 3x + 2 at x = 2 %3D

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Q: Find the tangent line to the equation: f(x) 3x2 + 2x-1, when x= 2 %3D

A: Using equation of tangent formula.

Q: Find the equation of tangent line to the curve f(x) = x² at x = 3.

A: Topic = Derivative

Q: Find the slope of the tangent line to the curve 1x² − 2xy + 1y³ = 13 at the point (4,3).

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Q: Find the slope of the tangent line to the curve 2x² 4xy + 4y³ = 10 at the point ( − 1, 1).

A: SOLUTION-

Q: Find the equation of the tangent line to the curve f(x) = x³ln (x + 1) at the point (0, 0).

A: The given curve is: f(x)=x3 ln(x+1)

Q: Determine the slope of the tangent line to the curve (x² + y² – 2x)² = 2(x² + y²) at (2, 2).

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Q: Find the equation of the tangent line to the curve g(x) = 3x² – 8x + 2 at the point (1, -3).

A: The equation of the curve and the point is given as,