If the slope of an arbitrary curve y=f(x) at a point p0(x0, f(xo)) is S. So do you think the slope of the same curve on another point, such as p1(x1, f(x1)) will be same? Why explain in detail?

Q: [3] If the curve is defined by y = x* – 8x3 + 22x2-24x+9, then what are the value/s of x for which…

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Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

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

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Q: Find the points on the graph of y = x2 + 3x − 7 at which the slope of the tangent line is equal to…

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Q: At what points does the equation of the line tangent to the curve y=1/x have a slope equal to −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: 5. Find an equation of the line tangent to the curve y = 3x² 1 and parallel to the line 2x – y + 3 =…

A: Explained below

Q: Find the equation of a line normal to the graph of y = 3x+5/x−1 at x = 3

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Q: What is the slope of the tangent line to the graph of y=x4-3x2+x+2 at x=2? b)What is the…

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Q: Find the slope of the line tangent to the graph of x^2+2xy^2+3y=31 at the point(2,-3)

A: The slope of the tangent line can be calculated by using the derivative of the function at the point…

Q: If y=mx+b is the equation of the tangent line the curve y = x- 3x +5, which is parallel to the…

A: We will solve the problem

Q: The slope of the curve f(x)= at x =1 is

A: given function :

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

A: Given that y'=-y5xdydx=-y5x

Q: 17. Given the curve y = 3x³ – 4x² +7, find the slope of the tangent line at the point when x= 3.

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Q: At the two points where the curve x² – xy + y² = 36 crosses the x-axis, the tangents to the curve…

A: Given equation of the curve is: x^2 - xy + y^2 = 36 ..................... (1) Differentiating above…

Q: 10. Find the slope-intercept form of the equation of the line tangent to the graph of y arctan(9x)…

A: Given y = arc tan9xand x=39here we find the slope - intercept form of the equation of the line…

Q: Therefore, the curve y = x* - 2x2 + 2 has horizontal tangents at x-0, 1, and -1

A: Just compute the derivative and equate it to zero.

Q: Determine slope of a curve y = x³ + 1 at x = 1

A: Given,           The slope of the curve y=x3+1  at x=1.

Q: Find the equation of the family of curves whose slope at any point (x,y) is 3x2+4

A: To find: the equation of the family of curves whose slope at any point (x,y) is 3x2+4  We know that…

Q: Find the slope of a line tangent to the curve of the given equation at the given point. y = x2 - 3;…

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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: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: Determine slope of a curve y = x³3 + 1 at x = 1

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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 equation of the family of curves whose slope at any point (x,y) is given and which passes…

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Q: The slope of the curve y = (5x² + 8x + e)eje at x = 0 is

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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: Find the member of the curve whose slope at any point is 2e** and passes through the point (0, 1)

A: We need to find the member of the curve whose slope at any point is 2e^(4x) and passes through…

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

A: First derivative of a function represents the change in function or slope of the function and second…

Q: What is the slope of the tangent line that touches the graph of In y + e2a-1 = 3y – 4x at the point…

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Q: Are there any points on the curve y = x - e^-x where the slope is 2? If so, find them.

A: To determine the point where the slope of the function is 2.

Q: 9. Find the points on the graph y = 7x - where the slope of the tangent line is parallel to x-2 28x…

A: To find- Find the points on the graph y = 7xx - 2 where the slope of the tangent line is parallel to…

Q: What is the slope of the tangent line that touches the graph of In(y)+e2x-=3y – 4x at the point (A 1…

A: The solution are next step

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: 4. Find the slope of the given function y3 = 4x with points (1, 2) using long method. Plot the curve

A: The solution are next step

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

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Q: Find an equation of the tangent line to the graph of y = 2x² + 3 that is parallel to the line 8x - y…

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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: B. Find the slope of the curve at the given point. 16. 2x²-3x+1 at (2, 3) 17. =3x²-2x+1 at (-1,6)…

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

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangent…

A: To find the x-intercept we plug y=0

Q: At what point does the graph of the function f(x) = x³ – 3x has horizontal tangent ? Find equations…

A: a) Points are (1,-2) and (-1,2) b) Lines are y=-x-1, and y=-x+3

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A: To find the equation of family of curves whose slope is given .

Q: 1) Find the slope of the line tangent to the graph of y=x²+1at(2, 5).

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Q: What is the equation of the curve passing through the (1, 16) and having a slope at any point (x,y)…

A: Given- 2xyx2+3 To find- The equation the curve passing though the (1,16) and slope at any point x,y…

Q: Find the equations of the line tangent to the curve y = x³ + x , where the slope is equal to 4.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.