The line tangent to the graph of g(x)= x^3 - 4x + 1 at the point (2,1) is given by the formula: L(x) = 8(x - 2)+1 These functions are graphed below. Which of the following statements are true? Select all that apply.

Q: What is the derivative of the function  x - 7x(x^1/2) ——————      x^1/2 Use quotient rule and…

A: The quotient rule of differentiation is as shown on the whiteboard.

Q: Find the derivative of f(x) = 2x²+3x-1 if f'(-1)

A: Given: fx=2x2+3x-1

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: 13

A:

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A: For the inflection point, second derivative is equal to zero.

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A: By the fundamental theorem of calculus if we have F(x)=∫f(x)dx then F'(x)=f(x). In some cases an…

Q: Find the slope and an equation of the tangent line to the graph of the function at the specified…

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Q: Match the function from the left side to its derivative. 1. x16 -4x-5 3 a. 2. 15 b. 3. ** 15x4 с.

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Q: Using the criterion of the first derivative, find the graph of the function: F(x) = 114 (x*) + 4,…

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Q: f(x)= (7x¹-5x-2)

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Q: sketch the graphof the function and state its domain. f (x) = 4 ln(x − 2) + 1

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Use the definition of the derivative to solve.

A: Given,

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A: We will use following properties of f(x) to draw its graph  # vertical asymptotes are vertical…

Q: Example 3: Find the root of: f(x) = x' - 3x+1 in the interval [0,1]?

A:

Q: Find the slope m of the line tangent to the graph of the function f(x) = 5 - 6x at point (-1, 11)

A: Given:  f(x)=5-6x                y=5-6xDidderentating y=5-6x   with respect to 'x'  and substituting…

Q: OF(x)= - 2x3+ 84x2-72x on 7- -6x²+48 x-72=0

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Q: Find the derivative. g(x) = (4x – 2)° – Vr + 8

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Q: Find the derivative using the formal definition f (x) = 3x2- 4x – 2

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Q: Find the points on the graph of f(x) = 2x3 + 15x2 - 84x + 12 where the tangent is horizontal. List…

A: we have to find the points on the graph of the function f(x) = 2x3 + 15x2 - 84x + 12 where the…

Q: The graph of f(x)=2x^3+6x^2−144x+6 has two horizontal tangents. what are the positive and negative…

A: See the details solution in below

Q: 1. Find the derivative of f(x) = 3x³ + 2x using the limit definition.

A: We have to find derivative using definition.

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

A: Given: f'(x)=-2x8-x2,    2,7 Integrate the given function to obtain the function f(x). The formula…

Q: Graph f(x) x'- 3x-9x + 2. 3r2

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Q: Find the slope of the line tangent to the graph of the function defined by f(x) = x2 – 3x + 4 at…

A: It is given that, f(x)=x2-3x+4   Slope of any function or tangent of any function is defined as the…

Q: Find the function of the derivative f'(x)= -12x+5 and with the graph passing through (-2,5)

A: Given, f'(x)= -12x+5

Q: Use the definition of derivative to find f(x) = 2-x+2x^2

A: Given,          fx=2-x+2x2

Q: Find a formula for a function that has vertical asymptotes x = 3 and x = 9 and horizontal asymptote…

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Q: The graph of a polynomial function, f(x), is shown above. In the interval shown, how many times with…

A: We know that for any functionfx, the second derivative of fx cross the x-axis means second…

Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

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Q: Find a formula for a function that has vertical asymptotes x = 6 and x = 8 and horizontal asymptote…

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Q: In(&x³) f(x) = 1-9e-* -2x 1-9e 2

A: Topic- derivative

Q: Find the derivative using the definition for the function f(x) 4 +8x-5x2.

A: Limit defination of derivative f'(x)=limh→0f(x+h)-f(x)h

Q: Use definition to find the derivative of the function f(x)= 2x-3x2 at x = 3 %3D

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Q: Make a sign diagram for the first and the secon derivatives and then graph the function…

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Q: f (x) = - 4x² - 6x x²+3

A: The given function is f(x)=4x2-6xx2+3. Find the derivative of the function. Here we use the…

Q: -f(x)=√√5x² +2

A: Please see the answer below.

Q: 5. Sketch the graph of y = x3 + 5x2 + 3x - 4 by using the properties of the derivative.

A: Find f' (x) then we check f(x) increasing Or decreasing.

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: Does the graph of y = sqrt(x) - ln x, x> 0, have an inflection point? Try to answer the question…

A: To determine if the function has an inflection point.Part (a) By GraphingPart (b) By Calculus

Q: Find the function with the given derivative whose graph passes through point P. F'(x)=2x-3, P(5,5)

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Q: Find the smallest positive root for the given function by using the false position method with…

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Q: How do you find the derivative of f(x)=5/1-8x using the definition of a derivative?

A: The given function is f(x)=51-8x

Q: Graph the tangent line to the function f(x) = –3x³ – 2x² – x + 3 at the point (-1, 5). Place point A…

A: Given that the function  is    f(x) = -3x3 - 2x2 - x + 3  Here we have to find the tangent line at…

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) > 0  from graph  Function is increasing…

Q: 13x

A:

Q: Q3\ Find the second derivative of the funetion F(x)= 3x + 2x - 6x2 -4

A:

Q: 9. Suggest a function that would have a derivative of f'(x) = 24x² + 6x – 10. Explain how you…

A: The derivative of a function id given as f'(x)=24x2+6x-10......(1)