Let f(x) 3D х? — бх. (A) Find the slope of the secant line joining (2, f(2)) and (9, f(9)). Slope of secant line = (B) Find the slope of the secant line joining (5, f(5)) and (5 + h, f(5 + h)). Slope of secant line = (C) Find the slope of the tangent line at (5, f(5)). Slope of tangent line = (D) Find the equation of the tangent line at (5, f(5)). y =

Q: Find equations of the two tangent lines to the graph of f(x) = 2x2 that pass through the point (-1,…

A: Here, the given curve is: f(x)=2x2 To find two tangent lines that pass through (-1,-6)

Q: Find the slope of the tangent line to the curve - 3x² + 2xy + 2y 3 - 38 - at the point (4, 1).

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Q: Find the slope of the tangent line to the curve - 3æ² ³ = - 199 3x? + lœy+ 3y at the point (1, – 4).

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Q: Find the slope of the tangent line to the curve 2x + 2xy + 2y = 32 %3D at the point (-4, 2).

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Q: At what point on the curve x 3t2 + 1, y = t3 - 5 does the tangent line have slope ? (х, у) -

A: We have given curve as x=3t2+1         ⋯⋯1y=t3-5           ⋯⋯2 From the equation (1) and (2), on…

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Q: Find the point on the curve y=x√x for which the tangent line to the curve is perpendicular to the…

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Q: Find the slope of the tangent line to the curve - 3x + lay+ 3y = 199 | %3D | at the point (1, – 4).

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

A: Curve y=ax3+bx2+cx+d is tangent to the line y=3x+8 at the point (-2,3). The curve y=ax3+bx2+cx+d has…

Q: Find the equation of the tangent line  x2y-y3 + 6x= 8  at the (3, -2)

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Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

A: Topic - tangent lines to curve passing through Given point outside curve

Q: B. Find the slope and the equation of the tangent line to the curve 1. y = 4 - 3x at (- 1, 1) 2. y…

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Q: On the same axes, plot the curve y = 1x, the line y = x/8, and the tangent line to y = 1x that is…

A: Given curve is y=x. Let x,y be any point on the curve. Differentiate function with respect to x.…

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + 4y° 3 242 at the point (- 1, 4).

A: Given curve is -2x2+3xy+4y3=242. To find: Slope of the tangent line to the given curve at the point…

Q: Find equations for the lines that are tangent and normal to the curve at the point (1,1).. x³ + y² =…

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Q: At what point on the curve x = 3t2 + 2, y = t3 – 2 does the tangent line have slope ? (х, у)

A: Slope of the line = dy/dx To get dy/dx, first get dx/dt then get dy/dt. Now divide dy/dt by dx/dt.5

Q: Find the tangent plane to the equation 4x2 + 3y2 – y at the point (-4,-1,68) Z =

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Q: Find the slope of the tangent line to the curve - 4x – 3ry + 4y° = = 14 at the point (- 3, 2).

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Q: Let f(r, y) = - (5x² + 4xy+ y²). Then an implicit equation for the tangent plane to the graph of f…

A: Given function is, fx,y=−5x2+4xy+y2 To find the implicit equation of tangent plane to the graph of f…

Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

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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…

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Q: Verify that (4,1) on the curve x + /xy = 6 and find the lines that are tangent and normal to the…

A: Given that, the curve is x+xy=6. Differentiate the curve x+xy=6 with respect to x as follows,…

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Q: write the equati on of the tangent and normal line line of the curve. huow your soution 2 2 4. f CX)…

A: Given: fx=x3-3x+4 at 2,6

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Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: Determine the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (√2, −1/√2).

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Q: Determine the equation of the line tangent to the curve   at the point (-1,1) and reestablish a…

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Q: the equation of the tange

A: Given that: The equation of the curve x2 + 4y2 = 8. The equation of the line x + 2y = 8.

Q: Find the slope of the tangent line to the curve V3x+y+v2ry = Vi+v4 at the point (2, 1). The slope is

A: To find the slope we need dy/dx

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: Find the point (xo, yo) on the graph of y = x³ + 3x? + 8x – 3, at which the slope of the tangent…

A: To find the slope of the function we need y'y=x3+3x2+8x-3y'=3x2+6x+8

Q: Show that the tangent line to the curve y = x3 at any point (a, a3) meets the curve again at a point…

A: Proof: The given curve is y=x3. Obtain the derivative of the function as follows: dydx=ddxx3…

Q: Find the slope of the tangent line using the Definition of a Tangent Line for: Y= x + 5X at the…

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Q: Find equations of the two tangent lines to the graph of f(x) = x- that pass through the point (-1,…

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Q: Find all points (x, y) on the graph of y = with tangent lines perpendicular to the line y= 4x - 3.…

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Q: Find the slope of the tangent line to the curve -3x2 +3xy- 4y = - 247 %3D at the point (1, 4).

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Q: x4 C: y=-+ 3 x3 17 4 12

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Q: Find the point on the curve y = x³ + x2 – 1 where the tangent is perpendicular to the line y = -x

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Q: Determine the values of p, q, and r so that the function f(x) = px° + qx² + rx will have an…

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Q: Find the slope of the tangent line to the curve - 2x2 + 4ry – 3y - 63 at the point (3, 3).

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Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

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Q: write the equation of the tangent and normal line line of the curve. huow somtion your 1 . f(x) = -…

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Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent…

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Q: Find the slope of the tangent line to the curve – 4x - 422 3ry + 4y° = 14 - at the point (- 3, 2).

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Q: Find the equation of the line tangent to the curve 2(z² + y°)* = 25(z² – y²) at the point (3, 1).…

A: Suppose a line passing through with slope  m then equation of line is .