Suppose that f(2 + h) – f(2) = 3h² + 5h. Calculate: (a) The slope of the secant line through (2, ƒ(2)) and (6, f(6)) (b) f'(2)

Q: What is the slope of the tangent line to the graph of x-xy-4y2 +2x +4y 8 at (4, -2)?

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Q: Find the slope of the line normal to the graph of y=secx at x=π/4

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Q: What is the slope of the line tangent line to the curve x²y = y2 – 6x when x=2?

A: The given curve is x2y=y2-6x. Substitute x=2 in the above equation and obtain that,…

Q: For Exercise, find the slope of the secant line pictured in red. 6--y = f(x) %23 (3, 4) (1,1)" ! 2 3…

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Q: y = vx² – 9

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Q: If ƒ′(x) = 3x + 2, find the slope of the line tangent to the curvey = ƒ(x) at x = 1, 2, and 3.

A: Slope of the tangent line is the derivative of the given function at the given point. Therefore…

Q: Find an equation of the tangent line to the curve y=2x^2+3 that is parallel to the line 8x-y+3=0

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

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

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Q: Find equations of all lines having slope - 1 that are tangent to the curve

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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…

Q: Find an equation of the tangent line to the curve y= x3 – 3x2 + 5x that has the least slope.

A: Given    slope is 1st derivative

Q: Find the slope of the tangent line to the curve x² - xy - 2y³ 116 at the point (-2, 4).

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Q: Find the slope of the tangent line to the curve 4x + 4cy- 4y° 276 at the point (- 1,4).

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Q: Find the slope of the tangent line to the curve – 2a2 + xy + 4y³ = - 6 3 at the point (- 2, 1).

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Q: What is the slope of the tangent line to the curve 3x^3y^2−2y^3=−4 at the point (1,2)

A: To find the slope of the tangent line we need y' 3x3y2−2y3=−49x2y2+3x3(2y)y' - 6y2y'=0 [product…

Q: Show that the curve y = 7e* + 3x + 2x³ has no tangent line with slope 2.

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Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

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: Determine the slope of the line tangent to y = x+1 at x = 1 3x2

A: y = (x+1)/3x2 slope = dy/dx dy/dx = (3x2(1) - 6x(x+1))/9x4 slope at x=1 dy/dx = (3 - 6(2))/9 dy/dx =…

Q: What is the equation of the line tangent to the graph of y = x(1-2x)^3 at the point (-1,1)?

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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: Find the equation of line tangent of y=x4-2x2+1 at (2,9)

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Q: 2. What is the slope of the line tangent to the curve 8x³ – y² = 4 at the point (1,-2)? 3. What is…

A: Since first subparts question statement missed. Answer 2 and 3

Q: Find the slope of the line tan gent to the curve of 2y³ + xy + 1 = 0 at the point (-3, 1) .

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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: At what point on the curve y = 2x²– 3x – 1 is its tangent parallel to the line y = 5x + 2?

A: Given curve is : y=2x2-3x-1 And the given line is : y=5x+2 We need to find the point on the curve at…

Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: Find the equation of the tangent line  -4x2 + 3y2 = -24 ; (-3,2)

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Q: 5) What is the equation of the line tangent to y = 2x³ + 3x - 1 atx=0?

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Q: 9. at the point (-2,1) Find the equation of the line tangent to y = 2x2 + 1

A: We will find the equation of the line tangent in the following step.

Q: Find the slope of the line tangent to the graph of x2+2xy2+3y=31 at th epoint (2, -3)

A: To determine the slope of the tangent at the point (2, -3).

Q: Find the equation of the tangent line to the function f(x) 8vx - 4 at the point (64, 60). Provide…

A: Calculate the slope of the given function;

Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-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 equations of all lines having slope -1 that are tangent to the curve y = 1/(x - 1).

A: Given, y=1x-1 Slope,m=-1

Q: The slope of the tangent to the curve yx + y²x² -6 at (2,1) is

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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: Find the gradient of the curve y = x° – x2 – 8x – 2 at the point on - - - the curve whose…

A: As we know that; The expression for the gradient or slope; m=dydx And The Power law; ddxxn=nxn-1

Q: Show that the curve y =6x3 +5x -3 has no tangentline with slope 4.

A: Consider the following equation of curve: y=6x3+5x-3 Differentiate y with respect to x:…

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 the slope of the tangent line to the curve y 3x-8x + 7 at the point (-1,2). -3 3. -4 4

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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: 2. What is the slope of the line tangent to the curve 8x³ - y² = 4 at the point (1,-2)? 3. What is…

A: In 2 we need to find the slope of the line tangent to the given curve at a point.  in 3 we need to…

Q: Show that the line y = -10x + 20 is tangent to the curve y = x4 – 4x^3 – 5x^2 + 26x – 16.

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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: 2. Find the curve that passes through the point (1, 3) and whose tangent line at (x, y) has slope

A: Solve for the curve

Q: What is the slope of the line tangent to the graph of y=[9x^2]/[x+2] at x=1?

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Q: What is the slope of the tangent line to the curve 3y- 2-6-2xy at the point (3, 2)?

A: Given,           3y2-2x2=6-2xy     To find slope, let's differentiate. wrt.x           3.2y…