Q1) By using transformations of mother functions, sketch the following curves and determine the range. A) f(x) =3-e" B) f(x) = Ex -2

Q: Find the equation of the function f whose graph passes through the point (0, 8/3) am whose…

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Q: Q3/ Use the definition of derivative to find f'(x) where fx=- 3 X+1

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Q: use the definition of derivative to find f prime (x). f(x)= 3(2x-1)^3

A: Given function is fx=32x-13. To find the derivative of the function using definition of derivative.…

Q: Use formulas (1) and (2) and the power rule to find the derivatives of f (x) =3x/4 - 2

A: As the formulas (1) and (2) are not provided here. So, I solved by using the basic formulas of…

Q: Use formulas (1) and (2) and the power rule to find the derivatives of f (x) = -2x

A: To find the derivative of: f(x)=-2x Solution: f(x)=-2xOn differentiating both sides w.r.t x we…

Q: b) Use the definition of the derivative to find the derivative of f(x) = 4x³ + - at a = 1. 23

A: Given: fx=4x3+1x3; x=1 We know that ddxxn=nxn-1                                          ..1

Q: Find the equation of the tangent line to the graph of f(x) = -2(3x – 1)³ at . Show work or explain…

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Q: Find f'(x) using the definition of the derivative. 1. f(x)=x^3-1

A: We have given f(x) = x3-1 So using definition of derivative  f'(x) = limh→0fx+h-fxh So f(x+h) =…

Q: Use the definition of a derivative to find f ' x and f "x . Then graph f  ,f " ,f "' and on a common…

A: Given data: The function given here is f(x) = x3 - 3x. The definition of 1st order derivative of a…

Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: Find the equation of the tan gent line to the graph of the equation f(x) = 5x - 8x +12, at the point…

A: Here we are going to solve only one question and for the remaining question post the question again.…

Q: The function f is given by f(x) = -1-e-. What is the equation of the line tangent to the graph of f…

A: Given data: The given function is f(x)= -1- e-x. The slope of the tangent line is f'(x)=5. The…

Q: Suppose that the slope of the line tangent to the graph of a function f at the point (x, f(x)) is…

A: Given: The  slope of  a curve:   To determine: The equation of the curve f(x)

Q: 5. Use the definition of derivatives to find f'(2) given that f(x) = 2x² -r+1

A: According to our company guidelines we are supposed to answer only one question since you have asked…

Q: Find the slope of the line tangent to the graph of f(x) = 4 - xatx = 2. Provide your answer below: m…

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Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent.

A: Given that  f(x)=(-8x)/(√(2x-1))  The function has a horizontal tangent  To find the point at which…

Q: sketch the graph of a function f whose derivative f' has the given description:f'(x) > 0 for x…

A: Given that f'(x) > 0 for x > 3 and f'(x) < 0 for x < 3. There are many possible graph to…

Q: Find the tangent line to f(x) = , when x = 1. Give your answer in fully 2-x simplified slope…

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Q: Use limits to compute the derivative.   f ′(4) if f(x)=3x3 f ′(4)=?

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Q: 4 -4 -3 2 4 -2

A: See from the given graph of the function fx, the graph becomes parallel to x axis at the points x=-2…

Q: 1 . Use the definition of the derivative to compute f'(x) if f(x)

A: We use the limit definition of f'(x)

Q: Given f(x) : , find f'(-1) using the definition of a derivative. x-2 Provide your answer below: f'(…

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Q: sketch the graph of a function f whose derivative f' has the given description. f'(x) > 0 for x…

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Q: Sketch the graph of the derivative for function shown.

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Q: Determine the point(s) at which the graph of -8x f(x) = 2х- 1 has a horizontal tangent. (х, у) %3D

A: Solution - The derivative of a function is 0 at a point where the tangent is horizontal. Let us…

Q: 1. Find the slope of the line tangent to the graph of the function defined by f(x) = 4 + 2x - x2 at…

A: As you mentioned only 1 solved

Q: Find the slope of the graph of the function at the given point. F(x) = 4x5 + 5x - sin(x), (0, 0)…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: Given, f'(x)= sec22x; π2, 0

Q: IT Aiswer Find the derivative of the function f(x) = 10arcsin(x- 9).

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Q: Find the equation of the tangent line to the graph of g(x) = f'(x) at x = -1 when f(x) = 5x³ + 2x² +…

A: Here, f(x)=5x3+2x2+2x

Q: 16. Use the limit definition of the derivative to find the instantaneous rate of change for the…

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Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: Determine the derivative of each function using the limit definition. 1. Y = 2 – 7.x

A: Topic = Derivative As per guidelines , At  a time only one question can be answered out of different…

Q: Qs, find Thi domain of He function

A: Given the given function is fx=1-x. Domain→it is the set of input values at which the function is…

Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

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Q: Given f(x) = 2, find f' (1) using the definition of a derivative. x-2 Provide your answer below:…

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Q: Find the derivative and state the domain of f(x) = In(x + 4) %3D

A: In this question, concept of derivative is used. Derivative The derivative expresses the rate of…

Q: 4 3. Лх) — Зх - 5 %3D

A: Given that  f(x)=4/(3x-5)^2  To find the derivative of f(x)

Q: Sketch the graph of y= x²+ - by using the properties of the derivative. 2

A: To sketch the graph

Q: f(x)

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Q: What is the limit that will calculate the derivative f'(2) for the function f(x)= x-1

A: solution of the given problem is below...

Q: Suppose that the slope of the line tangent to the graph of a function f at the point (x, f(x)) is…

A: Using integration.

Q: use the limit definition of the derivative to show that the derivative of  f(x)=x^2+9x is…

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Q: Find equations of the two tangent lines to the graph of f(x) = x that pass through the point (-1,…

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Q: 3 1. 15. f(x) = 4 *+ %3D 4

A: Given,f(x)=14x+34

Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Given            fx=x-33x+4

Q: 3. If f(x) = 2x² + 3x find f'(a) by using definition of derivative at a point a=4

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Q: Consider the function f(x) = x3 + 4, and the point (1, 5). Write the equation of the line tangent to…

A: Compute the slope as follows.