Let f(x) = 1 - (x + 3) + 2x. Find all values of x for which f(x) is at least 4.

Q: Let h(x) = f(x) – g(x). If f(x) = 5x² and g(x) = 2x³, what is h' (1)?

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Q: (a): Find the critical points of the function f(x) = 8x² – 16x.

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Q: Let F(x) = 2x^3 - 5x + 1 Explain, by using the Intermediate Value Theorem, why this function has (…

A: A polynomial function is everywhere continuous. A point x= a is said to be a x- intercept of a…

Q: Find the intervals where the function f(x)= x3- 3x 2+3 is increasing and intervals where the…

A: The given function is f(x)=x3-3x2+3. It is required to find the interval in which the function is…

Q: Show that f(x)=x5-x3-1 has a zero between 1 and 2.

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Q: Let f(x)= Vx+3 and g (x) =- x+3 Determine 3.

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Q: On which interval(s) is the function f(x)=(12/5)x5-3x4-8x3+5 increasing?

A: Given function is,

Q: A function f(x) = v1 – x² is

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Q: f(x)= 2x² – 8x- 3 on the given interval [1,3].

A: Given f(x)=2x2-8x-3 on [1,3]

Q: Let h(x)=f(x)g(x). If f(x)=x2−3x,g(0)=−1, and g′(0)=−4, what is h′(0)?

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Q: Let h(x)=f(x)g(x) where f(x)=2x2−4x, g(−2)=4, and g′(−2)=−5 what is h′(−2)?

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Q: Find the critical numbers of the function. a. f(x) = x³ + 6x2 – 15x

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Q: Find real values of x for which f(x) = 0. f(x) = x3 − x

A: Given: fx=x3-x To find the real values of x for which fx=0. Solution: Put fx=0 and then solve for x.…

Q: Let f(x)=3x^2+7x-4 and g(x)=9x^2-5x+1. Which equation shows h(x), where h (x)= f(x)-g(x)?

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Q: b- Determine the critical point of the function f(x) = x5 – 5x* + 5x³ –- 1 %3D

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Q: Find the function f(x) that satisfies the conditions f1) - | and f'x)= 2x+1

A: Given that: f(x) satisfies f(1)=1and f'(x)=2x+1(x2+x+1)3 We have to find the function f(x)

Q: The fixed-points of f(x) = (x² + 2) are_ and

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Q: Let k(x)=f(x)g(x)h(x). If f(x)=−3x+4,g(x)=−x+4, and h(x)=−3x2−4x+3, what is k′(x)?

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Q: Consider f (x) =x³ – 6x²+9x +3 defined on the closed interval .At which value of x does the absolute…

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Q: The function f(x) =2x² – 3.x² – 12.x is increasing on: |

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Q: Find f(0), f(-3), f(2x+3) for the function f(x)= -2x^2+x-1.

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Q: Let k(x)=f(x)g(x)h(x). If f(x)=−2x−3,g(x)=−3x+3, and h(x)=−3x2+x+1, what is k′(1)?

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Q: Find the critical numbers of the function  f(x) = x3 + 6x2  - 15x

A: Solution -  Given function is given as- f(x) = x3+6x2-15x…

Q: Find the values of x for which the function f (x) = x −7/x^2 + 3x −70 is continuous.

A: Topic:- function

Q: Let h(x)=f(x)+g(x). If f(x)=6x and g(x)=3x^2, what is h′(−1)?

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Q: Explain why the function has at least one zero in the given interval.

A: The given function is f(x)=x3+5x-3 ,  0,1

Q: Find the absolute maximum and minimum values of f(x) = 2x³- 3x2 – 12x for 0 <x < 3.

A: First we find the critical points of f(x) and then local extremum points of f(x). Then comparing the…

Q: Let h(x)=f(x)g(x). If f(x)=−2x^2+2x+3 and g(x)=−x^2−3x−4, what is h′(−1)?

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Q: Find the intervals on which the function f(x)=x3+1x3 is strictly decreasing.

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Q: Find the interval on which f(x)=x2-4x+3 is increasing and the interval on which it is decreasing

A: Answer

Q: The fixed-points of f(x) = (x² + 2); are and

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Q: Find a function f(x) such that f'(x) = 6x² – 3 and f(0) = 1 - %3D f(x) =|

A: Given:     f'(x) = 6x2 - 3    f(0) = 1

Q: Let f(x) = 8x3 - x4 + 4. 1. Find the interval of concavity.

A: Find the second derivative of f(x) and equate it to zero f(x)=8x3-x4+4 f'(x)=24x2-4x3…

Q: The fixed-points of f(x) = (x² + 2) are and

A: Solution :  The fixed point of the function f(x) is  f(x) = x  Since, given function is  f(x) = 1/3…

Q: 1. Let f (x) = 2x² – x – 1 and let g(x) = x – 1 Which statement is true?

A: Given, f(x)=2x2-x-1 and g(x)=x-1

Q: The domain of f(x) = v2x + 1 is

A: According to the question, we have to find the domain of the above algebraic function fx=2x+1. The…

Q: Define f (x) = 4 + x – x² and g(x) = 5x 3. %3D - - Find the value of (f•g)(-1).

A: Explained below..

Q: find the extreme values on the interval f (x) = x2/3 − 2x1/3, [−1, 3]

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Q: Let h(x)=f(x)g(x). If f(x)=−3x2+2x−3 and g(x)=−3x2+4x+3, what is h′(1)?

A: Given:h(x)-f(x)g(x)f(x)=-3x2+2x-3g(x)=-3x2+4x+3

Q: Find the critical numbers of the function. f(x) : 6x2 – 9x %3D

A: given f(x)=6x2-9xdiffrentiate the function to calculate critical pointsf'(x)=12x-9

Q: find c such that f(x)=-0.2x2-3x+c has a maximum value of -224. what is the value of c

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Q: Find all the possible x-values of f(x)=√x - 2

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Q: Explain why the function has at least one zero in the given interval.

A: To explain why the given function has at least one zero in the given interval.

Q: Find a and b so that the function 2.3 – 5x² + 2, x -2 f(x) = ax + b, is both continuous and…

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Q: Let h(x)=f(x)−g(x). If f(x)=5x2 and g(x)=2x3, what is h′(1)?

A: Consider the given functions, fx=5x2 and gx=2x3 Since it is given that hx=fx-gx so substitute the…

Q: Find the absolute extrema of the function g(x) = -10x/x^2+9 on the interval (-5,2)

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Q: Find f (x) for the function f(x) = х-2 ·In x+5

A: This question can be solved using the concept of inverse of function.

Q: The fixed-points of f(x) = (x² + 2) a and

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Q: Find the absolute maximum and minimum values ​​of the function f(x)=x2−3x2+1 in the interval [-1/2,…

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Q: Find f (x) given f "(x)= 6x² +8x³ – x and the initial condition f(-1)=- 2

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