Find the equation of the normal line to the given curve at the specified point. (Hint: The normal line is perpendicular to the tangent line. If you recall from algebra, two lines are perpendicular if their slopes are negative reciprocals.) Include y= in your answer.  y=(x4-1)√x (1,0)

Q: The slope to the tangent line of a curve is given by f(x) = x2 -9x + 12. If the point (0, 9) is on…

A: Given that slope equation and we find the equation of curve. I.e.  df(x)/dx = x2 - 9x + 12. And also…

Q: 4. For what values of x does y² – 2x3 – 12x? = 0 have horizontal tangent lines? A. x = 0 only В. x =…

A: The value of x for function Horizontal tangent lines ?

Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…

A: y=x2-2x-3

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

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Q: (3) Find the equation of the line tangent to f(x) = 2x³ - 2x2 +1 at x = 1. [Hint: f'(a) is the slope…

A: We find the slope of f(x) at x=1 by finding f'(1)

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 slope m of the tangent to the curve y = 9 + 5x² – 2x3 at the point where x = a. 10а + 6а?…

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = (e4x −…

A: We first have to find y'We apply exponent rule and chain rule.y'= 8(e^(4x))*(e^(4x)) -4)

Q: he slope of the line tangent to the curve y = x -8x3 + 22x2 - 24x +9 at x=1 is (a) -2 (b) 2 (c) 0…

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Q: Find the slope of the curve, equations of the tangent and normal lines to the given point. 8x y at…

A: Solution

Q: Find the equation of the tangent line and normal line to the curve ? = √? − 3 and whose normal line…

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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: For what value of x is the tangent line to the curve y= x² – 6x +5 horizontal? (A -3 3 D none of the…

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Q: f(x) = 4x^2 - 4x^3 + 4 What is the slope of the tangent line at x=2?   What is the equation of the…

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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: Find the point on the graph of y = x3 such that the tangent at the point is parallel to the line y –…

A: Consider a graph: y=x3……1   Equation of line parallel to the tangent of above equation is:…

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: Determine the equation of the line tangent to the curve at the given point. y = In(x? – 5x + 1), (5,…

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Q: For what value of x is the tangent line to the curve y= x2 – 6x + 5 horizontal? A B) -6 -3 D none of…

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Q: Find the slope of a line tangent to the curve of the given equation at the given point. y=(x^3)/4;…

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Q: 1. Find the slope of the line normal to the curve at (1, 2). y=v5x-x? 4 A. 3 В. -4 С. D. E. None 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: Find all values of x at which the tangent lines to the graph of x4 - 2x2 + 15 4 y = are…

A: y = x44 - 2x² +15>   To find All Values of x where tangent lines to given Curve perpendicular…

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

A: The given function is y=x3 and the point is 2,8.

Q: Find the equation of the line tangent to the graph of x3 + y3 = -5xy + 7 at (1,1).  The equation of…

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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: Find the slope and the equation of the tangent line to the graph of the given function at the given…

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Q: 9.Reduce the general equation of the given straight line y-x 3=4 to the normal form.

A: y-x3 = 4for normal form equation should be in the form x cosα +y sinα = p∴-x3 +y = 4

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: Find h'(-3) if h = f o g, f(x) = -8x? + 6 and the equation of the tangent line of g at -3 is y = 7x…

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Q: For what value(s) of x does the slope of the line tangent to the curve y=-x'+3x +1 take on its…

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Q: find an equation of the tangent line to the graph of the given point. f(×)= √x(x-8), (16,32)

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Q: 1. Find the slope of the given curve at the indicated point a. y = x³ – 4x? + 3, at x = 2 b. y =, at…

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Q: 9. Find the points on the graph y = х-2 7x - where the slope of the tangent line is parallel to 28х…

A: Given-  Consider the graph y=7xx-2. To Find- The points on the above graph , where the slope of the…

Q: Find the equation of a tangent line to the graph of the function g(x)=2x−x2g(x)=2x−x2 that is…

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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: find equations for the lines that are tangent,and the lines that are normal, to the curve at the…

A: Solution:- The given curve is  x+xy=6  ......(1) and point (4,1) we have to find equation of the…

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

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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: At what point (s) is the tangent line to the curve y²=2x³ perpendicular to the line 4x-3y+1=0

A: Given y2=2x3⇒ y=2x3

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: The equation of a curve is given by f(x) = (6x² − 7) (2x + 6). What is the slope of the tangent line…

A: The slope of tangent line on a curve f(x) that touches the curve at x = c is m = f'(c).

Q: For what value of x is the tangent line to the curve y= x2 -6x +5 horizonta? A -3 B C) none of the…

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

A: we can obtain the equation of curve by forming a differential equation . we know that the slope of…

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

A: Given problem is : Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn…

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: B. find the slope of the tangent to the curve at the given point 1. y= x-6, (1, - 2) 2. y = 3x -5x.…

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Q: 2. Write the equation of the tangent line to the curve y = x2 -x-2+ 2 at the point P(1, 2). 3. Use…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…