Solve the following problems, Show your Complete Solutions (This is all about Basic Calculus: Slope of the Tangent Line to a Curve). a. Find the equations of the tangent and normal lines to the curve y = x² + 2x + 3 at x = – 1. (Note: A normal line is a line perpendicular to the tangent line at the point of tangency.) b. Find the equation of the tangent line to the curve y = x² – 2x – 3 that is parallel to the line x + y = 1. c. Find the equation of the tangent line to the curve y = x² – 3x + 4 that is perpendicular to the line x – y = – 1.

Q: It is given to you that an equation of the tangent line to the graph of y=g(x) at x=16 is 5x+8y=56…

A: It is given that, an equation of the tangent line to y=g(x) at x=16 is 5x+8y=56.

Q: What is the slope of the tangent line that touches the graph of In y +es-1 = 3y – 4z at the point…

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Q: b. If B(x) = /g(x), what is the equation of the tangent line drawn to B(x) when x = 1? %3D

A: b) if B(x)=g(x)we have to find the equation of tangent line drawn to B(x) when x=1   differentiate…

Q: Determine an equation of the line tangent to the curve at the given point. 4x² + 4xy + 3y 51, (3,1)

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Q: Find the equation of the line which is tangent to the granh of y .3r2 2r + 4 at tho

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Q: Consider the following equation. 4x3 + 3y2 = 52 Step 2 of 2: Find the slope of the tangent line at…

A: The given equation is 4x3+3y2=52. Evaluate dydx using implicit differentiation as follows.…

Q: Find the coordinates of the point on the graph of y = x^2− x + 3 at which the tangent is parallel to…

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Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: Given,          x=t2-4 , y=t3+6t , t=3To find: The equation of the tangent line.We know that,…

Q: Find an equation of the line tangent to the given curve at a. y = x3 – 4x2 + 2x – 1; a = 2

A: Slope m of the tangent will be given by dydx Therefore, dydx=ddxx3-4x2+2x-1 ⇒dydx=3x2-8x+x…

Q: The graph of ax + b f(x) = (æ – 1)² has a horizontal tangent line at (–3, –). Find a and b.

A: For horizontal tangent line at a point derivative of the given curve is zero , just used it and…

Q: 1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: 3. Find the equation of the line tangent to the curve f(x) = 3r²+4r+1 at the point (1,8).

A: To find the equation of the tangent line to the curve f(x).

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: At what point on the graph of y = is the tangent line parallel to the line 2x-4y = 3? (B) (5.) m…

A: Given the curve y = x2/2 we need to find the point where the tangent of curve y is parallel to the…

Q: Consider the following equation. Step 2 of 2: Find the slope of the tangent line at (-1, 2). 2x² +…

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Q: The equation of the tangent line to the curve at the given point. x2 v2 2-13 = (1, 1) is %3D 100 4…

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Q: 11. What is the y-intercept of the line that is tangent to the graph of y =-x +4x at (1, 3)? a. -2…

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Q: Solve the following problems a. Which of the following are the coordinates of a point where the…

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Q: Given that f(3) = -1 and f'(3) = 5, find an equation for the tangent line to the graph of y = f(x)…

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Q: It is given to you that an equation of the tangent line to the graph of y = g(x) at x = 9 is 7x +…

A: 7x+12y=-21 is the tangent to the graph of y=g(x) So, at x=9 the y value of the tangent will give…

Q: 7. Find the slope of the tangent line of the graph of 2ry+ y? = 3.x² – 4 at the point (-1, 1).

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

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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: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

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Q: Given that f(3) = -1 and f'(3) = 5, find an equation for the tangent line to the graph of y = f(x)…

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Q: The equation of the tangent to the curve f(x)=x3−6 which is parallel to −2y+54x−3=0 is...

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Q: 3. For what value of x will the slope of the tangent to f(x) = 3**e* +5x +17 be equal to 5?

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Q: Find an equation of the line tangent to each of the following curves at the given point. 4x 11, 12 y…

A: The given equation of curve is y=4xx2+3                  ……(1) Now differentiate the equation (1)…

Q: Solve what is asked in the following problems. Write your solutions and box your final answers 1.…

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Q: c. Find the equations of the line tangent to the curve y = x³ + x, where the slope is equal to 4.

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Q: What is the equation of the tangent line to the curve y = √2 +16when x = 3? V x-10y +47=0 3x-25y-116…

A: SOLUTION-

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: Solve the following problems. Show the complete solution. 3. What is the equation of the tangent…

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Q: Given that x² + y? = (2x² + 2y² – x²)? Find an equation of tangent line to the curve at point (0,…

A: The formula to differentiate the product of two functions, f(x) and g(x) with a common variable is…

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: Consider the following equation. x4 + 3xy – 2y4 = -4 Step 2 of 2: Find the slope of the tangent line…

A: Slope of tangent line = dy/dx

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: If y = x* - 4x° - 8x², the points at which the tangent to the curve is parallel to the x-axis are A.…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

A: Solution of given question is written in below steps.

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = −1 and B ′(24) =…

A: Given thaty=B24 x=24y=B24 =-1B'24 =-14To :find equation of tangent line Solution :equation of line…

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: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: By using slope formula and equation of tangent line, we find the required equation of tangent line.

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 y' and the slope of the tangent line to the graph of (3x - 4y)7 = 2y2-7 at the point (3,2).…

A: The slope of equation is defined in terms of m=dy/dx

Q: Find an equation of a line tangent to the graph of h(x) =s at x-2 y=6x+13 O у-бx+13 y=6x+12 O…

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Q: If the slope of the tangent to f(x)= a(x-1) + bx at the point (2, determine the values of the…

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Q: What is the slope of the tangent line that touches the graph of In(y) +e2-1=3y – 4x at the point 3 A…

A: We have to choose the correct answer from the given information according to the given information

Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: use property of chain rule to find the slope and equation of tangent line

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = 0 and B'(24) = -…

A: Given,         y=Bx at x=24 if B24=0 and B'24=-14.

Q: (1) Find the equation of the line tangent to k(r) = (x³ – 5)(x² + x) at the point (1, –8). Write…

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