Determine whether Rolle's theorem can be applied for the function f(x) = x* – 3x² ;[-3,3] .If so, find “ c ", if not explain why?

Q: Ax, y) = In(x +y)

A: In this question, we have to find the domain and range of f(x,y)=lnx+y As we know that the domain of…

Q: Apply Rolle's theorem for the function f(x) = 8x² – 32x + 24 over the interval [1,3]. %3D

A:

Q: ): Apply Rolle's theorem for the function f(x) = 9x² – 36x + 27 over the interval [1, 3]. Justify…

A: Given :- Apply Rolle's Theorem for the function fx = 9x2 -36x + 27 over the integral 1,3.

Q: Consider the function defined on the indicated interval. f(x) = 2x – 30x + 144x – 220, [5, 8] %3D…

A: To find maximum and minimum of the given function in interval [5, 8] fx=2x3−30x2+144x−220

Q: Find the values of a and b that make the following piecewise defined function both continuous and…

A:

Q: Verify that Rolle's Theorem can be applied to the function f(x) = x3-8x2+19x-12 on the interval…

A:

Q: he domain of the function f(x) = Vx+5 is In(3-x) %3D

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Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws…

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Q: Give a characteristic that the two functions f(x)=x and g(x) = 2' have in common.

A:

Q: III. Verify if the function is continous at the point. 1. f(x) = x³ – 3x² + 2x – 5 at x = 0 %3D %3D…

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Q: Differentiate f(x) = a4x4 -3ax² with respect to x. Assume that a is a constant. f'(x) =

A: f(x)=ax4-3ax2 differentiate with respect to x

Q: Verify that Rolle's Theorem can be applied to the function f (x) = x^3 - 8x^2 + 17x - 10 on the…

A: Given,          Verify that Rolle's Theorem can be applied to the function fx=x3-8x2+17x-10 on the…

Q: Let f be defined as follows: x2 +5 for x > 5, Зах f(x)3D for xs5 For what value of a is the function…

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Q: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

A:

Q: /Sketch the Function Y=Sgn(x) + Sgn (x-) and Finat its domain and vang es

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Q: 2. Determine whether the function y= -x5 + x3 – 1 is even, odd, or neither. Justify your ans wer.

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Q: Let f(x) = x^2 −x −2. Using the Intermediate Value Theorem, explain why this function has (at least)…

A: The function is  f(x)=x2-x-2

Q: Apply the intermediate value theorem  evaluate the function f(x)=x^4+8x+3 at each endpoint of the…

A: Given,         The function is fx=x4+8x+3 at each endpoint of the interval -1,0.

Q: Explain if the function is continuous or not for the given number a. if x > 1 f(x) = {1 if x = 1…

A: topic - limits and continuity

Q: Find the value of a that makes the following function differentiablefor all x-values

A:

Q: Use the definitions of increasing and decreasing functions to prove that       f(x) = x3 is…

A:

Q: Find

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Q: Let ƒ be the function given by ƒ(x) = (x-2)²(x+3). For what values of x is f not continuous?

A: The given function is fx=(x-2)2·(x+3)(x-2)·(x+1) We have to find the values of x, for which f is not…

Q: Given f(x) = Vx and g(x) = |x – 2|, find 9. Determine the domain of the function in interval…

A: Given function :

Q: Find the length of the are of the function x² = 4y from x = -3 to x = 3.

A:

Q: Consider the function f(x) = z + 6

A: Givenf(x)=1x+6

Q: How to use the standard y = f(x) notation to indicate that (a, b) is an element of the function f?

A:

Q: Use Intermediate Vaule Tun to show that the functions f(x) = x^3 and g(x) = 2x + 3 intersect at at…

A:

Q: III. Verify if the function is continous at the point. 1. f(x) = x³ – 2x² + x – 5 at x = 0

A: f(x) is continuous at x=0 if- limx→0-f(x)=limx→0+f(x)=f(0)

Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

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Q: Show that the function g(x) =x |x | has an inflection point at (0,0) but  g " (0)  does not exist.

A: Given function:                                 g(x)=x|x|   To find out the Inflection point=?…

Q: Determine whether the function is differentiable at x = 2.

A: The given function is fx=x2+1,x≤24x-3, x>2. Sketch the graph of the above function as shown…

Q: Let f(x) = ∥x∥. Find out its conjugate function f ⋆ and prove your conclusion.

A:

Q: function

A: We are given a function : f(x)=x2-2x+2x-3 We have to determine the domain of given function where…

Q: Consider the function f(x) = i + x². How does this function essentially behave for large positive…

A: The Given Function f(x) contains rational function x/(x2+1) and polynomial function function…

Q: Verify that Rolle's Theorem can be applied to the function f (x)= x3 – 8x2 + 17x – 10 on the…

A: Given  Y = X³-8X²+17X-10  Rolles theoram Rolle's theorem states that when a function is continuous…

Q: Differentiate the function. f(x)  = In 1/x

A: Given: The function fx=ln1x, To find: The differentiation of given function.

Q: Are there any values of r for which the function A is discontinuous? Why?

A: We have to find out

Q: Find the domain of the function using interval notation. f(x) = -2x (1- 1) (r – 7) To enter oo, type…

A:

Q: Verify that Rolle's Theorem can be applied to the function f(x)=x3−8x2+17x−10 on the interval [1,5].…

A: Given: The given function is f(x)=x3-8x2+17x-10. The objective is to verify that Rolle's theorem can…

Q: determine whether the piecewise-defined function is differentiable at x = 0.

A: to determine if the function is differentiable we have to check if it's differentiation is equal…

Q: The piecewise function f(x) is defined below. f(x) = {kx² - 4, Is-2 x+ 2, xS-2 x>-2 For what value…

A:

Q: Redefine the function f to make it continuous at x = 0. -8x + 36 + x (х — 4) ; x + 0,4 f(x) = 4; x =…

A: Consider the condition for continuity.

Q: IV. Verify Rolle's theorem for the function: f(x) = x2 – 5x + 6 on [2,3] а.

A:

Q: Evaluate f''(c) at the point. f(x) = (x2 - 5)(x3- 5), c = 1

A:

Q: Verify Rolle's theorem for the function 2x2 – 18x + 29 on the interval f(x) = [2, 7].

A: Given,          The function is fx=2x2-18x+29 on the interval 2,7.

Q: Find the domain of the function using interval notation. f (x) = -2a (x – 3) (x – 5) | | To enter…

A: soution:-f(x)=-2x(x-3)(x-5)To find the domin of f(x)The domain of a function is the set of all…

Q: Which of the following functions passes through the point (0,12) and satisfies f'(x)=8 ?

A:

Q: Evaluate the given piecewise function at the given points 2x +1, x 2 1 f(x) = %3D x2 +3, x< 1 at…

A: We need to find value of f(-2) and f(6) for piecewise function

Q: 3 Show that the function f(x) = Vx – 5 is one to one function.

A: The given function is: fx=x-53

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.