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Elena L [17]
3 years ago
10

Find the critical points, domain endpoints, and local extreme values for the function

Mathematics
1 answer:
aliina [53]3 years ago
8 0

Answer:

a) x = -3, b) x = 0, x = -6, c) x = 0, d) x = -6

Step-by-step explanation:

a) Let derive the function:

f'(x) = \frac{10\cdot x \cdot (x+3)-5\cdot x^{2}}{25\cdot (x+3)^{2}}

f'(x) is undefined when denominator equates to zero. The critical point is:

x = -3

b) f'(x) = 0 when numerator equates to zero. That is:

10\cdot x \cdot (x+3) - 5\cdot x^{2} = 0

10\cdot x^{2}+30\cdot x -5\cdot x^{2} = 0

5\cdot x^{2} + 30\cdot x = 0

5\cdot x \cdot (x+6) = 0

This equation shows two critical points:

x = 0, x = -6

c) The critical points found in point b) and the existence of a discontinuity in point a) lead to the conclusion of the existence local minima and maxima. By plotting the function, it is evident that x = 0 corresponds to a local maximum. (See Attachment)

d) By plotting the function, it is evident that x = -6 corresponds to a local minimum. (See Attachment)

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Ksju [112]

Answer:

the probability that a sample of 4 bags will have a mean weight less than 9.8 pounds is 0.05

Step-by-step explanation:

Given the data in the question;

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standard deviation s_x = 0.24 pounds

sample size n = 4

The bag weights are normally distributed so;

p( x' less than 9.8 ) will be;

p(  (x'-μ_x' / s_x')   <   (9.8-μ_x' / s_x')  )

we know that;

μ_x' = μ_x = 10

and s_x' = s_x/√n = 0.24/√4

so; we substitute

p(  z  <  ( (9.8 - 10) / (0.24/√4)  )

p(  z  <  -0.2 / 0.12   )

p(  z  <  -1.67   )

{ From z-table }

⇒ p(  z  <  -1.67   ) = 0.0475 ≈ 0.05

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3 years ago
Solve the following system of equations using substitution. What is the value of y?
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Joseph has 22 gallons of fertilizer. He uses 7 quarts to fertilize his plants.
nata0808 [166]
Joseph would have 81 quarts of fertilizer left
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F(x)=24x+7 What is the domain of f
yarga [219]
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hope this helps, God bless!
7 0
3 years ago
Help please show work
BARSIC [14]

Answer:

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Step-by-step explanation:

4 0
3 years ago
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