Mr.jones is planning to plant grass and place a fence in a small area for his dog the rectangular dimensions are 12 x15 feet the
2 answers:
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Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
<u>Algebra I</u>
- Average Rate of Change:
Step-by-step explanation:
<u>Step 1: Define</u>
Interval -1 ≤ x ≤ 3
a = -1, b = 3
f(a) = f(-1) = 4
f(b) = f(3) = -4
<u>Step 2: Find Average</u>
- Substitute in variables [ARC]:
- Substitute:
- [Fraction] Subtract/Add:
- [Fraction] Divide:
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.
