For f(x) = 7x2 - 7, find the number c in (-4, 4) guaranteed by Rolle's Theorem. (Use symbolic notation and fractions where needed.) C =

Q: 2x + 3, if For f(x) %3D (3x²- 11, if 17) f(5) = 18) 3f

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Q: x + 4 if f = 2r3 +1, find f(1). 5x – 4 -

A: Given,

Q: Find the particular solution determined by the given condition 314 f'(x) = 3x -6x; f(1) = -6 II

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Q: If f(x) = Jx-3 then f(-3) + f(12) is

A: We can make it easier for you

Q: If f(x) = 3x2 + 5æ, what is f(2)?

A: f(x)=3x2+5x Put x=2 f(2)=3(2)2+5(2)

Q: Find the values of k for which f(x) = kx3 -9kx2+9x+3 is increasing on R

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Q: Generate the approximation formula 1 f'(x) × - [4f(x+ h) – 3f(x) – f(x+2h)] 2h with the error term.

A: The objective is to generate the approximation formula,

Q: For x 2 0, show that 1S v1+x³ <1+x°. Explain your answers in detail.

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Q: For the f(x) = −x3 + 3x + 6 determine the coordinates of the turning point(s) and any point(s) of…

A: Given that f(x) = −x3 + 3x + 6 To determine the coordinates of the turning point(s) and any point(s)…

Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

A: Given that, f''x=3x3-14x2+8x For what value of x is fx concave down.

Q: If f'(x) > 3 for all x and f(2) = 5, what can you conclude about f(4)? %3D

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Q: Given f1x2 = ax + bcx + d find f -1 1x2. If c ≠ 0, under what conditions on a, b, c, and dis f = f…

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Q: If f(x)= 2x2 – 5x + 4 for what values of x is 2f (x) = f(2x)? -

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Q: What is the value of x at which f(x) = -5x2+4x+17 has an extremum?

A: We have to find for what value of x it gives extremum

Q: If F(x) = x2 - 3x + C and F(-1) = 4, what is the value of C?

A: Given: Fx=x2-3x+C  and F-1=4

Q: Given that f(x)=x^2+3x-70 and g(x)=x-7, find (f-g)(x) and express the result in standard form

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Q: For the f(x) = −x³ + 3x + 6 determine the coordinates of the turning point(s) and any point(s) of…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: f(x) = { kx+3, IF X<2 LyK-3x, IF X72

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Q: Given, F(x) = 2x+3/4x+5 for x ne-5/4; f^-1(x)

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Q: For f(x, y) = 2x3 + x²y2 - 5y3 + 10,

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Q: Determine the error term of for the formula: f'(x)  ≈ (1/4h) [f(x+3h) - f(x-h)]

A: In order to find the error term of the given expression, first find the value of f(x+3h) and f(x-h).

Q: Given f(x) = 3x° + kx – 10, and x – 2 is a factor of f(x), then what is the value -- of k?

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Q: Suppose we want to form an interpolant at equally spaced points xo = 0, x1 = h, and x2 = 2h of the…

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Q: For Ax) = x – 2x+ 7, find (A) ſa) (В) Да + h) (C) ſa+ h) – Ka) f(a+h)-f(@) h±0 h

A: Authoring guidelines:…

Q: Given that f(x) = 3x²- 3cx +2, find c such that if f(x) is divided by (3x – 1), the remainder will…

A: Using synthetic division we have to find the value of 'c' for which the following function when…

Q: The function f(x) =is 1-z2 Is 9+z2

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Q: What is r′(x) if r(x)=70x^5/2^x?

A: rx=70x52xTo find r′(x)

Q: 2) 1 V1-x² dx

A: The given integral,      ∫11-x2dx

Q: For the f(x)=−x3+3x+6f(x)=−x3+3x+6 determine the coordinates of the turning point(s) and any…

A: See the attachment

Q: For the f(x) = -x3 + 3x + 6 determine the coordinates of the turning point(s) and any point(s) of…

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Q: If f(x)=x3−2x+5f(x)=x3−2x+5, what is the value of f(2)f(2)?

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Q: Find f '(a) for f(x) = 3 − 2x + 4x2

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Q: What is the coefficient of the term contaning the variable h when f(x +h) – f(x) is performed, and…

A: Here we have to determine the coefficient of the term containing the variable h when f(x+h)-f(x)h is…

Q: An approximation of f'(2.5) is: -0.52083 -0.09895 -0.14825 -0.14583

A: We will apply the continuity of f(x) at point x=2 to find the unknown value of a  Next we will take…

Q: Given that f(x) = 5x 13x - 20x + 1. Which of the following is not true? %3D

A: f(x) = 5x3-13x2-20x+1 is a polynomial of degree 3 as the highest power of x is 3.

Q: (42) For f(x) = -2r" + 5x° – 12x²5 + 10, the degree of f"(x) is

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Q: If f(x) = (3x + 8) / (2x - A) and f(0) = 2, what is the value of A?

A: Given that, fx=3x+82x-A Also it is given that, f(0) = 2 We have to find the value of A.

Q: 14. For the function f(x)=ax³+bx² –5x+9 , determine the values of a and b so that s(-1)=12 and…

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Q: For f(x) = 25x3 + 50x2 - 4x +10 ... how do I find all values of x for which f(x) = 18 ?

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Q: Find the range of f{x}=x² +5x+6. O (00, 0) O (o, -1/4] O -1/4, )

A: Topic = Functions

Q: For the f(x) = -x2 +3x + 6 determine the coordinates of the turning point (s) and any point (s) of…

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Q: 7. Find y"' of ƒ(x) = 5x* + 4x³ – 7x2 8. Find y* of f(x) = x* – 5x? + 12x – 3

A: Take derivative 3rd time to given function In question (7) and 4th time to given function in…

Q: Given f(x) = In(x) + 7x2 - 19r, find f'(3). %3D

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Q: A car purchased for $20,160 is expected to depreciate according to the formula  f(x) = −1920x +…

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Q: For fx) = 2x+ 1 and g(x) = x2 - 7, find (f- g)(x). %3D O A. 2x2 - 15 O B. -x+ 2x- 6 O C. 2 - 2x- 8 O…

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Q: For f(x) = 2x + 1 and g(x) = x² – 7, find (f- g)(x). %3D O A. 2x2 - 15 O B. -x² + 2x- 6 O C. - 2x -…

A: Given that : The functions , f(x) = 2x + 1  and g(x) = x2 - 7 .

Q: Let h(x)=−2x^2+x+4/x^2+4x−1, what is h′(−5)?

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Q: Find the points of discontinuity for 3(x+2)2 a) h(x) x3 + 4x2 + x- 6 6x- x2 b) f(x) = 9 - x2

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Q: If f(x) = x²+4 and h(x) = 3x – 4, what is f(h(x²+4))? O9x*+68 O9x* + 60 O9x*+ 48x2+ 68 Oex*+ 48x? +…

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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.