A curve passes through the point (0, 9) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable.) v(x) =

Q: Find ​the slope of the curve at the given point​ P and an equation of the tangent line at P.…

A: solution:-y=-3-4x2point, P(x1, y1)=-3, -39slope=dydx=ddx-3-4x2=-8xat point -3, -39slope=-8(-3)=24

Q: The graph of y = f(x) has a y – intercept of 3 and the tangent line at the point (x, y) has an x-…

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Q: 3. The slope of tangent line at any point (x, y) on the curve is 3x²-2x+7. What is the equation of…

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Q: (a) Find the slope m of the tangent to the curve y = 1 + 4x2 – 2x³ at the point where x = a m = (b)…

A: Given equation of curve is: y=1+4x2-2x3

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

A: Given curve is,

Q: An equation of the tangent line to the curve C at the point (1, 2) is A у — 2%3 B y-2=2(x-1) ©…

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Q: The slope of the tangent line at any point (x, y) on a curve is 2yx. If the point (9, 3) is on the…

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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: 1.) Find the slope of the curve y^2=3x+ 1 at the point ( 1/3,0) Draw the graph of the Curve.

A: Slope of curve is given by its derivative   Given curve, y2=3x+1

Q: An equation of the line tangent to the graph of f(x) = x(1-2x)3 at the point (1,-1) is A. y = -7x+ 6…

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Q: Find an equation of the tangent line to y = f(x) when r = 2. The slope of the tangent line is f'(2)…

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Q: Determine all points on the graph of ƒ (x) = x* – x² – 1 for which a) the tangent line is…

A: Tangent line is horizontal at those points on the graph where derivative dydx=0 (1) At first we find…

Q: (a) Find the slope m of the tangent to the curve y = 9 + 4x2 − 2x3 at the point where x = a. m =…

A: Slope = dydx=m   ⇒ m=8x-6x2at x=a ⇒ m=8a-6a2

Q: A curve passes through the point (0,6) and has the property that the slope of the curve at every…

A: As we know that, the slope of the tangent line to the curve at Px,ya point is given by: dydx. Given:…

Q: A curve passes through the point (0, 8) and has the property that the slope of the curve at every…

A: solutionpaint=(0,8)slope=2y slope is true of y coordinateNow, we know that slope of the curveat o…

Q: The slope of the tangent line at any point (x, y) on the curve 3x2 -2x+ 7 and the point (1. 3) is on…

A: Given slope is 3x2-2x+7 and the point is (1,3)

Q: 3. Find the equation of the curve at every point of which the tangent line has a slope of 4.x. (a) y…

A: Slope = dy/dx

Q: The slope of the tangent line at any point (x, y) on the curve 3x2 -2x+7 and the point (1, 3) is on…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find an equation of the line tangent to the graph of G(x)=5 eX at the point (0,5). The equation of…

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Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the…

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Q: 5x=2 5. Find the member of the curve whose slope at any point is y+s point (3, 2) and passes through…

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Q: (a) If G(x) = 5x2 - x³, find G'(a) and use it to find equations of the tangent lines to the curve y…

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Q: A curve has an equation of y = x3 - 6x2 + 9x + 2. Find the point of inflection of the curve. а. (2,…

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Q: The equation of a curve is y = x + 2cos x. Find the x co-ordinates of the stationary points of the…

A: The given equation of the curve is  y = x + 2cos x

Q: The slope of the tangent line at any point (x. y) on a curve is 2x. If the point (9, 3) is on the…

A: the slope of the curve is the derivative of the function at that point.' here we have to form a…

Q: Given the curve y= x^3 - 4x + 1 . At what point on the curve have the smallest slope? * O (0,1) O…

A: The given curve is: y=x3-4x+1

Q: The graph of y = f(x) has a y – intercept of 3 and the tangent line at the point (x, y) has a x-…

A:

Q: 3. Find the equation of the curve at every point of which the tangent line has a slope of 4.x. (a) y…

A: Topic = Differential equation Correct option = d

Q: a. Determine an equation of the tangent line and the normal line at the given point on the curve. b.…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: ve passes through the point (0, 9) and has the property that the slope of the curve at every point P…

A: Topic:- application of integration

Q: (a) Find an equation of the tangent to the curve y = ex that is parallel to the line x – 4y = 1.(b)…

A: A straight line passing through the point has an equation where m is the slope of the line.…

Q: Find the slope of the following curve at x = 4. 1 y = х- 2 The slope of the given curve at x= 4 is

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Q: a. Find an equation for the secant line through the points where x has the given values. b. Find an…

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Q: 2. The slope of the tangent to a curve at any point (x, y) on the curve is. Find the equation of the…

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Q: The slope of the tangent line to a plane curve y=f(x) at the point (x,y) is given by 3 - 2 m=- + 16x…

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Q: A curve has a slope -X+2 of at each point (X,y) on the curve. Which of the following is an equation…

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Q: 9. (a) Find the slope of the tangent to the curve - 2x at the point where x = a. WE2S y = 3 + 4x2…

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Q: 20. Find the equation of the curve for which y" = x, and which through the point (1, 2) and the…

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Q: Find the slope and an equation of the tanger f(x) = /x + i slope equation

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Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 4x? - 8x + 4 has a tangent…

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Q: (a) If G(x) = 4x2 -x3, find  G'(a) and use it to find equationsof the tangent lines to the curve…

A: Gx=4x2-x3 Now differentiating with respect to x, we get G'x=42x-3x2=8x-3x2 Now slope of the tangent…

Q: (a) Find the slope, m, of the tangent to the curve y = 2 + 5x? – 2x3 at the point where x = a. m =…

A: On finding slope of the given curve we will differentiate 1st then using formula to find equation of…

Q: Find the point on the graph of y = 1/(1 + x2) where the tangent line has the greatest slope, and the…

A: The graph of the function is drawn below.

Q: (a) Find the slope m of the tangent to the curve y = 5 + 4x2 - 2x³ at the point where x = a. m = (b)…

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Q: Find the equation of the line tangent to the graph of x° + y° = - 2xy + 7 at (3, – 2). | The…

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Q: Find all points on the graph of y=(x+3)2 at which the tangent line is parallel to the line with…

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Q: (a) Find the slope, m, of the tangent to the curve y = 8 + 5x< – 2x° at the point where x = a. m =…

A: (a)   From the given problem:   y=8+5x2-2x3   As we know that the expression for the slope of the…

Q: A curve has a slope -X+2 of at each point (X,Y) on the curve. Which of the following is an equation…

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Q: 6. The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on…

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Q: Find the equation of the line tangent to the graph of 2 + y* = - 2xy + 13 at ( – 3, 4). The equation…

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