92. Use the definition of the derivative to prove that every quadratic function f(x) = ax² + bx +c has the property that its graph has a horizontal tangent line at the point x= 2a

Q: Determine the derivative of each function using the limit definition. 1. Y = 2 – 7x - 2 = 4 – 5x –…

A: f'(x) = limh→0 f(x+h)-f(x)h.

Q: Use one of the limit definitions to find the derivative of f(x) at x = 2. f(x) = 4x2

A: Explained below

Q: Find the slope of the tangent line to the graph of f(x) = x³ + x at x = 3 using the limits…

A: Given- fx=x3+x To find- The slope of the tangent line to the above function at x = 3 using the…

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: use the limit definition of deruvative to find the derivative of the given function. f(x)=5x2-3x+10

A: Given function f(x) = 5x2-3x+10using the limit definition of derivative , we have to find the…

Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: 5. Find the derivative by using the quotient rule. 3x - 2 (a) 2x +3 V+2 (c)- 3+2x (b) x +1 x+2 (d):

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Q: Use the definition of derivative to prove that In(1 + x) lim 1

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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: Use the limit definition of the derivative to show that if f(x) = x-4x2 Then f' (x) = 1 - 8x

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Q: Let f(x) = 4x² +. Use the definition of the derivative to find f'(1) %3D

A: To find- f'(1)

Q: Let Ax) = 8x_+ 3x² – x + 1_. a. Determine f (x). b. Use 13a to find the equation of the tangent line…

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Q: 2. f(x) = x2– 5x + 6 at x 2 --

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Q: Use the definition of the derivative to find f fx) = 2/(x + 3)

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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: 2) NOT use the short cut method). Use the result to find the slope of the tangent line at the point…

A: Topic:- Derivative

Q: What rule should be used in getting the derivative of a.)  f(x) = x^5 b.) h(x) = 3(x + 4)^3 c.)…

A: a. fx=x5 The rule used to get the derivative of given function is, ddxxn=nxn-1 The derivative is,…

Q: 5, i, Evaluate the first and second derivatives of the function z-2x4+3x3+2x-5 when x = 4.

A: We have to find the first and second derivative of the function z=2x4+3x3+2x-5 when x=4.

Q: Use the definition of the derivative to determine whether x 2 x, f(x) = is differentiable at x = 2.…

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Q: 17 Use the definition of derivative to evaluate the derivative of f(x) = 2x2 − 4

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

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Q: Suppose the derivative of the function y = ƒ(x) is y′ = (x - 1) 2(x - 2)(x - 4). At what points, if…

A: It is given that, the function f(x) has the derivative

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

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Q: Use the limit definition of a derivative to solve the following of f'(x) f(x)=4x2-x+1

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Q: Use the limit definition of the derivative of a function to find the derivative of f(x) = 4x %3D

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Q: Show, using the defniition of the derivative, that the derivative of f(x) = x^2 is f'(x) = 2x

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Q: Determine the value of X on which the derivative of the function Y = | 3x² + 4x + 1] does not exist.

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Q: By using the definition of the derivative find to f "(x) 3x3 +1 1 Ve +1 x +1

A: 1. We solve first order derivative of f(x)

Q: Show with the middle value theorem that the second derivative f'′ has at least one zero (for this…

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Q: Let f(x)=9−(4x^2+3x). Then according to the definition of derivative

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

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Q: Let f(x) = 4x² +. Use the definition of the derivative to find f'(1). %3D

A: To find the derivative of f(x) at x=1 using the derivative definition.

Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

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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: Let f(x) = 4x² + . Use the definition of the derivative to find f'(1). %3D

A: We can make it easier for you

Q: 1) Use the definition of the derivative to calculate the derivative off(x) = 3x2-5x+ 1

A: Find the derivative of f (x) = 3x2 –5x +1.

Q: Use the limit definition of the derivative to find f'(x). 2x f(x) = x+3

A: Given function is

Q: Determine the value of X on which the derivative of the function y 3x2 + 4x + 1| does not exist.

A: Giveny=|3x2+4x+1|y=|3x2+3x+x+1|y=|3x(x+1)+x+1|y=|(3x+1)(x+1)|Using modulus propertyy=|3x+1||x+1|

Q: Use the definition of the derivative to show that the derivative of y = f(x) = 2x² is f'(x) = 4x.…

A: Given that: y=f(x)=2x2

Q: In(&x³) f(x) = 1-9e-* -2x 1-9e 2

A: Topic- derivative

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: Find the slope of the line tangent to the graph of f(x) = 3x² - x- 5 at x = 1.

A: The equation of the curve is given by fx = 3x2-x-5 The point is x = 1 Formula Used: mtan = dfdxx=1…

Q: Show that f (x) = 1x-5| is NOT differentiable at 5 by using the definition of the derivative, (Start…

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Q: Find the equation of the tangent line to the function:   f(x) = 2x-1/x+2 when x=3

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Q: 2. Use the definition of the derivative to find f'(7) if f(x) = 4 + 3x – 2x.

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Q: Find the derivative of the function. f(x) = 2x In 2x %3D

A: Given, f(x)=2xln2x To find the derivative of f(x).

Q: Suppose f(x) = x^2−3x−5. Using the definition of derivative, compute f'(3).

A: Consider the given function: Here the objective is to find the derivative of the given function…

Q: Find an equation of the tangent line to the graph of f(x)=3x3+2x when x=1.

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Q: Use the limit definition of the derivative to find f'(16) for f(x) = the square root of x

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