Find the slope of the curve y = 2x2-3x at point (1,3) O 2 O 3 O -2 0 1

Q: 4. Find the equation for the line tangent to a. y=x²- 3 x + 5 at the point (2, 3)

A: We will find tangent equation.

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

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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 line tangent to the curve x + y3 = 4 at the point (3/3, –1).

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

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Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 7 at the point (3, 2.1). y =

A: Given curve is Differentiating with respect to x, we get

Q: Determine the equation of the line tangent to the graph of y = x° + 2x at the point (1, 3).

A: y=x3+2x   x1,y1 =1,3dydx=3x2+2slope of tangent at point1,3dydx1,3=312+2 = 5Slope of the tangent m =…

Q: Find the equation of the line segment tangent to the curve y−2x2−1=0y−2x2−1=0 which is parallel to…

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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: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ?

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Q: Find the slope of the curve x²+y²-6x+10y÷5=0 at point (1, 0)

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Q: Find an equation of the line tangent to the curve y = x²e*-3 at x = 3.

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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: 7. By definition find the slope of curve y = x2 – 2x – 3, at P(2, 3).

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Q: Find the equation of the family of curve whose slope at any point (x,y) is (x+1)/(y-1)

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Q: Write the equation for the curve that has slope of 2y/x for each point P(x,y) on it and passes…

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Q: Determine the slope of the curve x2+ y2– 6x – 4y – 21 = 0 at (0, 7).

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Q: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

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Q: Find the slope of the curve y=x4 at x=3.

A: Find the slope of the curve y=x4  at    x=3.

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

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Q: 4. Find the equation for the line tangent to a. y= x²- 3 x + 5 at the point (2, 3)

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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 slope of the curve x^2 + y^2 - 6x + 10y + 5 = 0 at point (1,0) * O 1/5 O 2/5 O 1/4 2 O O O…

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

A: given,y=3+4x2-2x3

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: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

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Q: Find the x value of the point on the curve y = 3x + 2 closest to the point (1, 0).

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Q: Determine the equation of the tangent to the curve y = x - e^-x that is parallel to the line 6x - 2y…

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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: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

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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 the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: ) Find an equation of the line tangent to the curve y = x²e²-3 at a = 3.

A:

Q: Find the equation of the tangent line to the curve y=x4 -14x2+17x+40 and perpendicular to the line x…

A: The equation of given curve is   y=x4-14x2+17x+40  On differentiating with respect to x, we get…

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: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

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Q: 14. Find the slope of the curve y = 2x3 – 3x at (-1 , 1)

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Q: Determine the equation of the line tangent to y = /1+x³ at the point (2, 3).

A: The given function is y=1+x3. Its derivative is obtained as, dydx=ddx1+x3=121+x3ddx1+x3=3x221+x3 at…

Q: Find an equation of the line tangent to the curve defined by x^3+6xy+y^5=21 at the point (2,1)

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Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

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Q: ]Find the x-intercept of the curve that passes through the point (0,2) and whose slope at (x,y) is…

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Q: Find the slope-intercept equation of the line tangent to the graph of y = 2lnx when x = 5. 2 -x-…

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Q: Determine the slope of the curve x2 + y2 – 6x – 4y – 21 = 0 at ( 0, 7 ).

A:

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

A: Given,