a. Normal to a curve Find an equation for the line perpendicularto the tangent to the curve y = x3 - 4x + 1 at the point (2, 1).b. Smallest slope What is the smallest slope on the curve? Atwhat point on the curve does the curve have this slope?c. Tangents having specified slope Find equations for the tangentsto the curve at the points where the slope of the curve is 8.

Q: The point P(S, -2) lies on the curve y = 2/(4 - x). (a) If Q is the point (x, 2/(4 - x)), use your…

A: Given the point P(5,-2) lies on the curve y=24-x & Q is the point x,24-x.

Q: 7. If y = find y' and use this result to find the points on the curve y = where the tangent line has…

A: slope of curve is given by dy/dx.

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

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Q: a) Find the point on the graph of y = e where the tangent line has slope -4. b) Plot the graph of y…

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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: Refer to the graph of y = f(x) = x² + x shown. a) Find the slope of the secant line joining (-4,…

A: Given:    f(x) = x2 + x

Q: Refer to the graph of y=f(x)=x2+x shown. ​a) Find the slope of the secant line joining (2, f(2)) and…

A: Please refer the attached image for complete solution.

Q: The point P (3,-8) lies on the curve y = x2 - 8x + 7. The point Q (x, x2 - 8x + 7) is also on the…

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Q: 17 2. The slope of a curve is (2x + b + and has a value of at x = 2. What is the 2х3 16 value of y…

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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: Solve the following problems, Show your Complete Solutions (This is all about Basic Calculus: Slope…

A: Solution:Given    y = x² + 2x + 3 To find Tangent and NormalFormula:tangent=dydxNormal=-1dydx

Q: Find the equation of the normal line to the given curve at the specified point. (Hint: The normal…

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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Q: Consider the following curve. y = 2x2 − 4x + 1 Find the slope m of the tangent line at the point…

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

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Q: (a) Find the slope m of the tangent to the curve y= 7+5x-2x at the point where x = a. m = (b) Find…

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Q: Consider the curve y = x2 – 3x + 8. (a) Find the slope of the secant line to the curve through the…

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Q: (a) Find the slope m of the tangent to the curve y = 5/Vx at the point where x = a > 0. m = (b) Find…

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

A: given: the equation of the curve is y=ex. we have to find the equation of the tangent to the curve…

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: # 4.) Line p (not shown) passes through A(0,–2) and intersects segment TI at the midpoint between T…

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Q: The point P(6, -4) lies on the curve y = 4/(5 – x). (a) If Q is the point (x, 4/(5 – x)), use your…

A: Finding the secant slope, tangent slope and equation of tangent to the curve at a given point from…

Q: 1. At which point on the graph of y = e" will there be a tangent line with slope m = 6? (a) at the…

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Q: with a slope of 2. 48. Find the equation of the tangent and normal lines to the curve y x+x² – x+1…

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Q: How do you solve a and b? I need the step by step solutions please

A: Given, function is

Q: (a) If x² + y? = 2x²y² , find y' in terms of both x and y. (b) Below is a graph of x2 + y? = 2x? y.…

A: Given equation is  x2+y2=2x2y2                      ..(1)

Q: Find two points where the curve x^2+3xy+y^2=47 crosses the x-axis. The tangent lines to the curve at…

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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: The point P (4, -2) lies on the curve y = x2 - 7x + 10. The point Q (x, x2 - 7x + 10) is also on the…

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Q: ind the value of y(1.5) given the equation of the family of curves at every point of which the…

A: given that the tangent line  of the family of curve has the slope m= 2y slope (m)= dydx=2y…

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: Find an equation of the tangent line to the function y= 4x at the point P(1, 4). Solution We will be…

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Q: Find the slope of the tangent line to the graph of the given function at the given value of x. Find…

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Q: I am so confused, question is in the picture.

A: According to the question,

Q: 3. The point P(2, -1) lies on the curve y- 1/(1 – x). (a) If Q is the point (x, 1/(I– x)), use your…

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Q: x at the point where x = a > 0. (a) Find the slope m of the tangent to the curve y = 5/ m = (4, 2).…

A: a. The given equation of the curve is y = 5/ x^(1/2).Compute the slope m of the tangent to the curve…

Q: (a) Find the slope of the tangent line to the curve at the point (1, 0). (b) Find an equation of the…

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Q: 3 The point P(3, -3) lies on the curve y = 2 - x 3 (a) If Q is the point (x, find the slope of the…

A: Recall: Slope of the secant line of two given points  x1,y1 and x2,y2 is given by  y2-y1x2-x1 .

Q: Q-4: The slope of the curve: y2 +x2 = y* - 2x at (-2,1). Is A: -1 В: 1 С: 2 D: none of them

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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: (a) Find the slope, m, of the tangent to the curve y = 9 + 5x2 - 2x3 at the point where x = a. m =…

A: Slope of the tangent is derivate of the given equation at that point.

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

A: Given,

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: ircular reception tent has a centre pole 25 feet high, and the poles along the outside are 10 feet…

A: slope of the line is given by

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: Find ​(a) the slope of the curve at the given point​ P, and ​(b) an equation of the tangent line at…

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

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