Find the equation of the curve that passes through (1,13) and having a slope of -4x at that point.

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

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Q: Estimate the slope of the curve at the indicated point. (2,5>

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Q: Find the equation of the line tangent to the graph of y = 4x (x - 4x + 5) at the point (2,8). y =

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Q: Find the equation of the line tangent to the given curve with the given slope. View the curve and…

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Q: Find cquation of the curve whose an slope at any point is y + 2x.

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Q: What is the equation of the line that passes through the point (2, –2) and has a slope of –? -

A: The line passes through point (2, -2) and has a slope of -12.

Q: Find the equation of a curve whose tangent line has slope 2x – 5 and the curve passes through the…

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Q: At what points on the graph of ƒ(x) = 6x2 + 4x - 9 is the slope of the tangent line -2?

A: Given: f(x)=6x2+4x-9  Now we find the slope  Therefore, differentiate with respect to x we get,…

Q: Estimate the slope of the curve at the indicated point. (-3,2> -1 Undefined

A: This question is based on slope at point.

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

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Q: Find an equation for the line perpendicular to the tangent to the curve y = x°- 16x + 6 at the point…

A: Given: y=x3-16x+6, 4,6 we know that equation of line which perpendicular to tangent at given point…

Q: Find the equation of the curve that passes through the point (8,4)(8,4) if its slope is given by…

A: Given :  Point ( 8,4) Slope (m) = dy/dx = 7x -8

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

A:

Q: Find the coordinates of the points on the curve y = x³ - 6x² + 14x – 12 at which the tangents have a…

A: We will differentiate with respect to x and equate the same to 5 and find the points.

Q: Find the equation of the curve whose slope at any point 3- у х - 2 and passes through (-1, 1).

A: We have to find equation of the curve such that slope equation is given by x-23-y and passes through…

Q: Find the curve having the given slope that passes through the indicated point y'= 2x - 5,(5,4).

A: We have the slope of the curve given as y'=2x-5dydx=2x-5 Now, ∫dy=∫2x-5dxy=2x22-5x+Cy=x2-5x+C

Q: Find the slope of the curve y = 2x3 - 3x2 - x +5 at (2,– 1)

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Q: this is a precalculus question

A: The initial height of the balloon is 131 meters. The balloon begins to ascend at a rate of 14 meters…

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: A hot air ballon is hovering 83 meters above the ground and begins to assend at a rate of 9 meters…

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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 all points on the graph of ƒ(x) = x3 + 9x2 + 19x - 10 where the slope of the tangent line is…

A: The derivative of xn is nxn-1 for n≠0. The derivative of f(x)+g(x) is f'(x)+g'(x). The derivative of…

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 all points on the graph of ƒ(x) = x3 + 9x2 + 19x - 10 where the slope of the tangent line is -5

A: Given: ƒ(x) = x3 + 9x2 + 19x - 10 The slope of the tangent line is -5

Q: Find the point on the Curve y =-3X that has a slope of -3 10

A: Given:

Q: Find the equation of the curve whose slope is given by 8 1 + x2 and the curve passes through the…

A: Solution

Q: Find the equation of a curve going through the point (3, 7) and having slope 4x² – 3 at (x, y).

A: Given ,Slope of curve is 4x2-3Thereforedydx=4x2-3Taking integationon both…

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: Find the equation of the curve that passes through the point (8, 6) if its slope is given by dy =6z-…

A: We have to find y

Q: Find an equation in slope intercept form that passes through the point (5,12) and has an x intercept…

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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 at the point where 0 = 4

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Q: Find an equation of the curve that passes through the point (0, 6) and whOse slope at (X, y) is X/y.

A: Given that: Slope of the curve at (x, y)=xy

Q: Find the slope of the line passing through the point (4,10) and perpendicular to the x+2y=5 line and…

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Q: At what point on the graph of ƒ(x) = -5x2 + 4x - 2 is the slope of the tangent line 6?

A: f(x)=-5x2+4x-2 slope = 6

Q: Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

A: Solution:find the equation of curuepasses through the point (0,4)slope of cwue is xydydx=xyy dy=x…

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 an equation of the curve that passes through the point and has the given slope. (Enter your…

A:

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: A hot air ballon is hovering 131 meters above the ground and begins to assend at a rate of 18 meters…

A: The balloon is 131 meters high. It is assending at a rate of 18 meters/second. y is the height of…

Q: Find the equation of the curve whose slope is – x/1 – x²and that passes through (0,7).

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Q: find an equation of the tanfent line to the curve at the given point y = 4x – 3x², (2, –4)

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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 slope of the curve y² = 3x + 1 at the point (- ,0). Draw the graph of the curve.

A: y2=3x+1 Differentiating with respect to x, we get 2y·dydx=31+0⇒2y·dydx=3⇒dydx=32y Now slope of the…

Q: The slope of the line tangent to the curve y=2x- 3 at point (1,-1) is 5

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find an equation for the line that passes through the point (2, –5) and has a slope of –3.

A: Line passes through the point 2, -5 with slope -3.

Q: Find the equation of the line through the points (5, 0) and (– 5, – 14) written in slope-intercept…

A: Given, The line is passing through the points 5, 0  and  -5, -14   We have to write the equation of…

Q: Find the curve having the given slope that passes through the indicated point. 2). y' 3 х2 — 2х - 4,…

A: Question 2,Given,            y'=x2-2x-4 , 3,-6To find : The curve using the point and slope.We know…

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)

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.