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vampirchik [111]
3 years ago
11

Sorry the quality is bad- I’ll mark brainlist

Mathematics
1 answer:
Sonbull [250]3 years ago
5 0

Answer: A and C

Step-by-step explanation:

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Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a)
Anna35 [415]

Rolle's Theorem does not apply to the function because there are points on the interval (a,b) where f is not differentiable.

Given the function is f(x)=\sqrt{(2-x^{\frac{2}{3}})^{3}}  and the Rolle's Theorem does not apply to the function.

Rolle's theorem is used to determine if a function is continuous and also differentiable.

The condition for Rolle's theorem to be true as:

  • f(a)=f(b)
  • f(x) must be continuous in [a,b].
  • f(x) must be differentiable in (a,b).

To apply the Rolle’s Theorem we need to have function that is differentiable on the given open interval.

If we look closely at the given function we can see that the first derivative of the given function is:

\begin{aligned}f(x)&=\sqrt{(2-x^{\frac{2}{3}})^3}\\ f(x)&=(2-x^{\frac{2}{3}})^{\frac{3}{2}}\\ f'(x)&=\frac{3}{2}(2-x^{\frac{2}{3}})^{\frac{1}{2}}\cdot \frac{2}{3}\cdot (-x)^{\frac{1}{3}}\\ f'(x)&=\frac{-\sqrt{2-x^{\frac{2}{3}}}}{\sqrt[3]{x}}\end

From this point of view we can see that the given function is not defined for x=0.

Hence, all the assumptions are not satisfied we can reach a conclusion that we cannot apply the Rolle's Theorem.

Learn more about Rolle's Theorem from here brainly.com/question/12279222

#SPJ4

8 0
2 years ago
Gum
yan [13]

Answer:

60 pieces

Step-by-step explanation:

The rate of pieces to packages is 15/1.

Multiply this rate by 4 to get the answer.

15 * 4 = 60

3 0
3 years ago
Read 2 more answers
for a company outing employees voted their preferences of bowling a movie or a baseball game seventy percent which is 56 employe
Novosadov [1.4K]
It would be 42 because 75 % of 56 is 42.
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3 years ago
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Find the range of the function for the given domain. f(x) = 2x - 7 ; {-2, -1, 0, 1, 2}
Studentka2010 [4]

The domain is a discrete set. So we will have a discrete range.

The range is a set containing:

f(-2)=-11

f(-1)=-9

f(0) = -7

f(1) = -5

f(2) = -3

Range = {-11,-9,-7,-5,-3}

7 0
3 years ago
Jade is thinking of a number. 3/4 of 200 is the same as 1/8 of her number. What number is she thinking of?
lorasvet [3.4K]

Answer:

1200

Step-by-step explanation:

3/4 of 200 = 150

150 is 1/8 of 1200

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3 years ago
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