y = (x-5)(x+1)

Q: Use the guidelines of this section to sketch the curve. x2 - 25 y = x2 - 5x

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Q: Determine the slope of the curve y =1/x+1 at point (−2,−1).

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Q: Find the equation of the line tangent to the graph of y = (x3 - 1)(x2 + 1)4 at the point where x =…

A: The Slope of the line at any point is given by the derivative of the function at that particular…

Q: Find the equation of the curve whose slope at any point (x, is given and which passes through the…

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Q: Find the equation of the curve for which y"= 2x³. The slope of the inflectional tangent at (-1, 3)…

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Q: Find an equation of the curve that passes through the point (1, 3), and has the given slope y′ =…

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Q: Use the guidelines of this section to sketch the curve.   y = 2√ x    -x

A: We will make a table for the function  x 0 1 4 9 y 0 1 0 -3

Q: Use implicit differentiation of the equations to determine the slope of the graph at the given…

A: Given: xy3=2 To determine the slope of the graph at the given point at x=-14 and y=-2. Solution:…

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

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Q: Find the equation of the tangent to the curve  y = -5x2 + 6x +7 at the point (1/2 , 35/4)

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Q: A3) Find the equation of the line tangent to the graph of f(x) = 5x+7x ---.

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Q: The slope of the curve defined by the equation y-x + x =-2 at the point (-1,0) is %D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the equation of the line tangent to the curve (x-2)^2=-4(y+3) at (2,-3)

A: Given data:     The expression for the equation of the curve is: (x-2)2=-4(y+3). The given point is:…

Q: The line y = -4x + 16 is tangent to the graph of 100 y : x + 6 at the point help (points)

A: Given the equation of a tangent line:

Q: Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the…

A: We have to find an equation of the tangent line to the curve at the given point.…

Q: Find an equation of the tangent line to the graph of the equation 6x - 5x8y7 = 36e6y at the point…

A: In this question, we will compute the equation of the tangent line of the given curve.

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: Use the guidelines of this section to sketch the curve.   y = (4 - x2)5

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Q: Graph the equation and its tangent. Graph y = x2 + 2x - 2 and the tangent to the curve at the point…

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Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y = dy…

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Q: Find a possible point of inflection of the curve y x +3x2 + 6x

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Q: Find the equation of the curve that passes through the point (0, 2) and has a slope of at any point…

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Q: equation of the curve that passes through the point (0, 6) and whose slope at (x, y) is x/y.

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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: Graph the equation and its tangent. Graph y = -3x2 and the tangent to the curve at the point whose…

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Q: Find an equation of the curve that passes through the point (0, 2), and has the given slope y′ =…

A: y'=x4y, (0,2) Formula ∫xndx=xn+1n+1+C

Q: Sketch the curve: y² = Xー4

A: A function is an equation that connects the variables x and y. In the xy plane, a function…

Q: Q3/ Line A with equation y = -8x - 18 is tangent to the curve with the equation y = 4x + 2x². Find…

A: Tangent line: If a line touches a curve at a unique point then the line is called tangent and that…

Q: Sketch the curve y = x/(x² – 9). Enumerate the steps in your solution.

A: as per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: Find the slope of the curve at the point (2,3) * x³ 2x + 1 3/2 1 O 1/2 O 1/4

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Q: Find an equation of the curve that passes through the point (1, 1), and has the given slope y′ = −…

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

Q: Find the slope of the curve: y= x^2/x^2 -1 at x=2

A: Slope of curve is the derivative of curve at the point .  Slope = m = ( dy/dx ) | x = a

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

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Q: Find the equation of the line tangent to the curve y =8/x2+4 at the point (2, 1).

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Q: Find an equation of the curve that passes through the point (1, −2), and has the given slope y′ =…

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Q: 2x at x =1 y = Зх-1

A: Find dydx as follows. y=2x23x-1dydx=22x3x-1-3x23x-12dydx=23x2-2x3x-12 Find dydx at x=1 as follows.…

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: The line whose slope is 3 is tangent to the curve y=x² + 3x + 2 at the point, O (3,-2) O (-3,2) O…

A: The line whose slope is -3 is tangent to the curve y=x2 +3x+2 at the point. Here slope and line…

Q: Find the equation of the line tangent to the graph of y = 4x'-9x-7 at the point (1,8).

A: Method to find tangent at a point of any curve.

Q: Determine the slope-intercept equation of the line tangent to the graph of y = 4x^2 - 7x + 1 at x =…

A: y=4x2-7x+1 We need to Determine the slope-intercept equation of the line tangent to the graph of the…

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: 2а3x at (a, a) ,2 x2+a²

A: Given curve is,

Q: Find equations of both lines that are tangent to the curve y = x3 - 3x2 + 3x - 3 and are parallel to…

A: The given curve is represented by y = x3 - 3x2 + 3x - 3 and are parallel to the line 3x - y =…

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,

Q: Find equations of both lines that are tangent to the curve y=x3 -3x2+3x-3 and are parallel to the…

A: Given, curve y=x3 -3x2+3x-3 and tangent are parallel to the line 3x-y=15.

Q: Locate the inflection points of the curve y = e²x²

A: The given curve is y=e2x2. The first derivative of y=e2x2 is, y'=ddxe2x2=2xe2 The second derivative…

Q: Find the equation of the line that is tangent to the graph of y= x^3 +4/x^2 at point (2,9)

A: The equation of tangent line to y=f(x) at (x0,y0) is y-y0=f'(x0)(x-x0)

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: