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3 years ago

The table shows some values of f(x) and g(x) for different values of x:

Mathematics

1 answer:

Helga [31]3 years ago

7 0

Answer:

(f + g)(2) = 10, (h – g)(2) = –9, (f × h)(2) = –12, (h / g)(2) = –0.5Step-by-step explanation:

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Find the absolute maximum and absolute minimum values of f on the given interval.

anyanavicka [17]

The question is missing parts. Here is the complete question.

Find the absolute maximum and absolute minimum values of f on the given interval.

$f(x)=xe^{-\frac{x^{2}}{32} }$ , [ -2,8]

Answer: Absolute maximum: f(4) = 2.42;

Absolute minimum: f(-2) = -1.76;

Step-by-step explanation: Some functions have absolute extrema: maxima and/or minima.

Absolute maximum is a point where the function has its greatest possible value.

Absolute minimum is a point where the function has its least possible value.

The method for finding absolute extrema points is

1) Derivate the function;

2) Find the values of x that makes f'(x) = 0;

3) Using the interval boundary values and the x found above, determine the function value of each of those points;

4) The highest value is maximum, while the lowest value is minimum;

For the function given, absolute maximum and minimum points are:

$f(x)=xe^{-\frac{x^{2}}{32} }$

Using the product rule, first derivative will be:

$f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )$

$f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )$ = 0

$1-\frac{x^{2}}{16}=0$

$\frac{x^{2}}{16}=1$

$x^{2}=16$

x = ±4

x can't be -4 because it is not in the interval [-2,8].

$f(-2)=-2e^{-\frac{(-2)^{2}}{32} }=-1.76$

$f(4)=4e^{-\frac{4^{2}}{32} }=2.42$

$f(8)=8e^{-\frac{8^{2}}{32} }=1.08$

Analysing each f(x), we noted when x = -2, f(-2) is minimum and when x = 4, f(4) is maximum.

Therefore, absolute maximum is f(4) = 2.42 and

absolute minimum is f(-2) = -1.76

8 0

3 years ago

What is an equation of the line that passes through the points (6, -3)(6,−3) and (-6, -5)(−6,−5)?

Amanda [17]

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3 years ago

8.15 = e + 6 Solving one step equations Addition and subtraction

Alex Ar [27]

Answer:

e= 2.15

Step-by-step explanation:

Subtract both sides by 6

2.15=e

Thus e is 2.15

Hope this helps!

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2 years ago

Joan flipped a coin 100 times during a mathematics experiment. The coin landed on tails 36 times. Based on Joan's results, which

Darina [25.2K]

It is A because it can’t be B and it can’t be C and it can’t be D so my answer is A

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3 years ago

What is the y-coordinate of point W? -2.5 -1.5 1.5 2.5

larisa86 [58]

Answer:

2.5 -1.5

Step-by-step explanation:

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3 years ago

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