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earnstyle [38]
2 years ago
14

Use a graphing calculator to graph f(x) = x+cos(kx). Use calculus to determine which values of k lead to a function with no loca

l maxima or minima. What conclusions can be drawn?
Mathematics
1 answer:
nataly862011 [7]2 years ago
7 0

Answer:

Below, you can see the graph of the function:

f(x) = x + cos(k*x)

for different values of k, as follows:

red: k = 1

green: k = 2

orange: k = 0.

Now let's find the values of k such that our function does not have local maxima nor local minima.

First, remember that for a given function f(x), the local maxima or minima points are related to the zeros of the first derivate of f(x).

This means that if:

f'(x0) = 0.

Then x0 is a maxima, minima or an inflection point.

Then if a function is such that the f'(x) ≠ 0 , ∀x, then this function will not have local maxima nor minima.

Now we have:

f(x) = x + cos(k*x)

then:

f'(x) = 1  - k*sin(k*x)

This function will be zero when:

1 = k*sin(k*x)

1/k = sin(k*x)

now, remember that -1 ≤ sin(θ) ≤ 1

then if 1/k is smaller than -1, or larger than 1, we will not have zeros.

And this will happen if -1 < k < 1.

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PilotLPTM [1.2K]

Answer:

Bc equals 17.

you must solve for BA and CA, because this is a isosceles triangle and isosceles have 2 equal sides.

BA = CA

then plug in what you find in for x

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3 years ago
Does a rotation preserve congruence
luda_lava [24]
No (random words to reach 20 characters lol)

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3 years ago
find the measure of the central angle of a circle if it's minor are length is 14π and the radius is 18 inches
MrMuchimi

Step-by-step explanation:

Length of arc of a circle is given as:

l =  \frac{ \theta}{360 \degree}  \times 2\pi \: r \\  \\  \therefore \: 14\pi = \frac{ \theta}{360 \degree}  \times 2\pi \:  \times 18 \\  \\ \therefore \:\theta =  \frac{14\pi \times \: 360 \degree }{2\pi \:  \times 18} \\  \\ \therefore \:\theta =  \frac{7 \times \: 360 \degree }{18}  \\  \\ \therefore \:\theta =  7 \times \: 20 \degree \\  \\  \huge \red{ \boxed{\therefore \:\theta =  140 \degree}}

Thus, the measure of central angle is 140°.

7 0
3 years ago
Someone help please
Likurg_2 [28]
Which one do you need help with?
8 0
2 years ago
Find the value of x using the diagram below. Round to the nearest whole number. Picture Attached.
VashaNatasha [74]
Both triangles are right triangles. x is the hypotenuse of the upper one. ThePythagorean formula  will give the value of x. One side is known, The other side we will find using the fact that the lower right triangle is isosceles. The hypotenuse of an isosceles right triangle has a length of \sqrt{2} times the length of one of the legs. In this case 14. So the hypotenuse of the lower triangle is also the short side of the upper triangle. Using Pythagoras

25^{2} +  (14 \sqrt{2}) ^{2} = x^{2}

625 + 392 =  x^{2}

 1017 =  x^{2}

32 = x

4 0
3 years ago
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