Please help! will give brainlist
2 answers:
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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.
Answer:
We conclude that the sum of two rational numbers is rational.
Hence, the fraction will be a rational number. i.e.
∵ b≠0, d≠0, so bd≠0
Step-by-step explanation:
Let a, b, c, and d are integers.
Let a/b and c/d are two rational numbers and b≠0, d≠0
Proving that the sum of two rational numbers is rational.
As the least common multiplier of b, d: bd
Adjusting fractions based on the LCM
As b≠0, d≠0, so bd≠0
Therefore, we conclude that the sum of two rational numbers is rational.
Hence, the fraction will be a rational number. i.e.