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rodikova [14]
3 years ago
15

Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x − ln 8x, [1/2, 2]

Mathematics
1 answer:
insens350 [35]3 years ago
4 0
The given function is 
f(x) =  x - ln(8x), on the interval [1/2, 2].

The derivative of f is
f'(x) = 1 - 1/x
The second derivative is 
f''(x) = 1/x²

A local maximum or minimum occurs when f'(x) = 0.
That is,
1 - 1/x = 0  => 1/x = 1  => x =1.
When x = 1, f'' = 1 (positive).
Therefore f(x) is minimum when x=1.
The minimum value is
f(1) = 1 - ln(8) = -1.079

The maximum value of f occurs either at x = 1/2 or at x = 2.
f(1/2) = 1/2 - ln(4) = -0.886
f(2)  = 2 - ln(16) = -0.773
The maximum value of f is
f(2) = 2 - ln(16) = -0.773
A graph of f(x) confirms the results.

Answer: 
Minimum value  = 1 - ln(8)
Maximum value = 2 - ln(16)


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Miya is picking up two friends to go the beach. She drives from her house to
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Answer:

Option (C)

Step-by-step explanation:

Coordinates of the point representing the location of Miya → (1, 10)

Coordinates of the point representing the location of Drea → (13, 1)

Coordinates of the point representing the location of Francine → (16, 1)

Coordinates of the point representing the location of Beach → (19, 4)

Distance between Miya and Drea = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

                                                        = \sqrt{(13-1)^2+(1-10)^2}

                                                        = \sqrt{144+81}

                                                         = 15 miles

Distance between Drea and Francine = \sqrt{(16-13)^2+(1-1)^2}

                                                               = 3 miles

Distance between Francine and Beach = \sqrt{(19-16)^2+(4-1)^2}

                                                                  = \sqrt{9+9}

                                                                  ≈ 4.2 miles

Total distance between Miya and the beach = 15 + 3 + 4.2

                                                                          = 22.2 miles

Option (C) is the answer.

5 0
2 years ago
What is the slope of the line?
Katyanochek1 [597]

Answer:

1

Step-by-step explanation:

slope (k) is the rise over run of the line

a way of finding the slope if you have two dots of the line is:

k \:  =  \frac{y2 - y2}{x2 - x2}

here the dots that belong to the line that you can most easily see are:

A(-6,0)

B(0,6)

by inserting the values into the euquation you get:

\frac{6 - 0}{0 - ( - 6)}  =  \frac{6}{6}  = 1

good luck with your maths solving

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3 years ago
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Answer:

14 cm

Step-by-step explanation:

The first step is to find the area of the triangular base. The formula for the area of a triangle is \frac{bh}{2}=\frac{10.2\cdot16.8}{2}=85.68. Now, you can divide the total volume by this to find the length. 1199.52/85.68=14. Hope this helps!

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3 years ago
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