a. Use the following information to graph the function f over the closed interval [-2, 5]. i) The graph of f is made of closed line segments joined end to end. ii) The graph starts at the point (-2, 3). iii) The derivative of f is the step function in the figure shown here. y' = f'(x) -2 3 -2 b. Repeat part (a), assuming that the graph starts at (–2, 0) instead of (-2, 3).

Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5 – x² AT (3,–4).

A: f(x)=5-x2 To find the slope of tangent, we can use two alternatives (1) Direct derivative (2)…

Q: 5. Find the equation of the tangent line to the curve of the function Y= 2x-x +2 at the point (1,3).

A: Given,  y = 2x3-x2+2   and the point 1, 3 We have to find the equation of the tangent line at the…

Q: Find an equation for the line tangent to the graph of f at (2,15), where f is given by…

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Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

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Q: Find the equation of the tangent line to the graph of the function f (x) - - Enter the exact answer.…

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Q: 5. Find the equation of the tangent line to the graph of the function f(r) = 5- z at the point where…

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Q: Find the equation of the tangent line to the graph of the function f (x) = (x² + 8) (x – 3) at the…

A: The gradient of the tangent at any particular point is given by :     f(x) = (x2 + 8) (x - 3)…

Q: The equation of the tangent line to the graph of f(x) = Vx+1 At the indicated point (3,2) is:…

A: By using the derivative and slope intercept form required tangent equation is :

Q: Find an equation of the tangent line to the graph of f (z) = -2² + 3z – 2 at the point (2, 0)

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Q: 9. What is the equation of the line tangent to the graph of the function f at the point (1,1)? f (x)…

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Q: 2. use implicit differentiation to find an equation of the tan- gent line to the curve r+2r'y+-50 at…

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Q: 4. Find an equation of the line tangent to g(x) = 3x² - x +1 at x= 1.

A: Given function

Q: 14. Find the equation of the line tangent to the graph of f(x) = 2x3-x + 1 at x = -1. %3D

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Q: 22. Find an equation of the tangent line to the graph of f(x) = 4 - x² at (a) (-1,3); (b) (0, 4);…

A: Given: f(x)=4-x2 To Find: the equation of the tangent line to the graph at a) (-1, 3) b) (0, 4)…

Q: Find an equation of the tangent line to f(x) = x² at the point (3,9).

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Q: 10. (a) Find an equation for the line tangent to f(x) = x³ + 4x² at the point x = 1.

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Q: Find an equation for the tangent line to the graph of y – 3xy + x2 +1 = 0 at the point (2, 1).

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Q: Find the equation of the line tangent to the graph of y = 3x cos x at the point (π, −3π).

A: Given Data: Equation: y=3xcosx Point: (x1, y1)=(π, −3π) The derivative of the given equation of…

Q: 3. Find the equation of the tangent line to the curve f (x)= (1+2x)'" at the point (0,1) in…

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Q: 2. Find the points on the graph of f(x) =- where the tangent line is horizontal. x2+2

A: Given f(x)=xx2+2we want to find the point on curve where tangent is horizontal

Q: Find an equation of the tangent line to the graph of the function at the given point. y = xsin(x),…

A: We tale ln on both sides then differentiate both sides with respect to x

Q: Find an equation of the tangent line to the graph of the function f defined by the given equation at…

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Q: The slope of the tangent line to the graph of the function y = 8VI - 4 at (16, 28) is O 1.50 O -1.75…

A: Given function is, y=8x-4

Q: 2. Find the equation of the tangent line for the function 2 f(x) = x2 + - 3 at a = -2

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = el-x,…

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Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

Q: 4 Let f(x) = 4x + x2 given by y = mx + b for . Then the equation of the tangent line to the graph of…

A: We know that if m is slope and (x1,y1) is point on line the equation of line is given as-  (y - y1 )…

Q: Find the equation of the tangent line to the graph of j f (x) =- -5e2* at the point (0, -5).

A:

Q: Find an equation of the line tangent to the graph of f at the given point.

A: Solution:Given          f(x)=sec-1(ex);              (ln 2, π/3)To find the equation of the line…

Q: 8) Find the equation of the tangent line to the graph of g(x) x3 7 at x = 2. -

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Q: 1) Find the slope of the tangent line to the graph of f(x) = x2 - 3 at the point (2, 1). %3D (8…

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Q: 15 Find the equation of the tangent line to the graph of f(x) at the point where x = 2 Vx3 – x + 3

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Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

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Q: Find the equation of the tangent line to the graph of f(x) = 1 at the point (2,1). x-1

A: Consider the graph of function, To calculate the slope (m) of the tangent line at the points (2,…

Q: 3. Given that the graph of f passes through the point (2,5) and that the slope of the tangent line…

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Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

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Q: Find an equation of the tangent line to the graph of f (x) = - at the point (1,2).

A:

Q: Find an equation of the tangent line to the graph of f(x) = e×/2 In(x) at its inflection point.…

A: The point of inflection is the point where the second order derivative of the function becomes zero.…

Q: The tangent line to y=f(x) at (1,-3) passes through the point (3,9). Compute the following: f(1)=?…

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Q: 2 Determine the equation of the tangent line to the graph of f(x) = Vx-12x at the point where x -3.

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Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

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Q: Find the equation of the fangent line to the graph of the function f (z) sin (3,/7) at the point…

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Q: 6. Find the equation of the tangent line to f(x)= = tan (2x) at the point (n/8, 1).

A:

Q: Find the equation of the tangent line to the graph of the function f(x)=x+1x−6 at the point (0,−16).

A: Equation of tangent is y-y1=m(x-x1) where m is the slope.

Q: Find an equation of the tangent line to the graph of the function (x)= Vx –7 at the point (23, 4).

A:

Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

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Q: 1. Find the equation of the tangent line to the graph of f (x) = x²e-* at x = 1. %3D

A: The given function is: fx=x2e-x In order to find the slope of the given function, find the…

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = e-X…

A: Given: f(x)=e-xln(x)

Q: The slope of the tangent line to the graph of the function y = 7VI - 3 at (9, 18) is O -2.00 O 1.83…

A: Solution

Q: 1. Use implicit differentiation to find all points on the graph of y3 – 3y = 2² + 3r +2 at which the…

A: When tangent is vertical then slope of tangent not defined