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3 years ago

Which interval for the graphed function contains the local maximum?

Mathematics

1 answer:

Kamila [148]3 years ago

8 0

Answer:

Step-by-step explanation:

Definition: Suppose that $f(x)$ is a function and $D(f)$ is the domain of $f(x).$ If $a\in D(f),$ we say that $f(a)$ is a Local Maximum on $f(x)$ if $f(a)\ge f(x)$ when $x$ is near $a.$ (See attached diagram for details)

From your graph you can see that the local maximum is nearly x=1.5, so interval [1,2] contains the local maximum.

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Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x3 and y = x. (10 points)

USPshnik [31]

See the graph attached.

The midpoint rule states that you can calculate the area under a curve by using the formula:
$M_{n} = \frac{b - a}{2} [ f(\frac{x_{0} + x_{1} }{2}) + f(\frac{x_{1} + x_{2} }{2}) + ... + f(\frac{x_{n-1} + x_{n} }{2})]$

In your case:
a = 0
b = 1
n = 4
x₀ = 0
x₁ = 1/4
x₂ = 1/2
x₃ = 3/4
x₄ = 1

Therefore, you'll have:
$M_{4} = \frac{1 - 0}{4} [ f(\frac{0 + \frac{1}{4} }{2}) + f(\frac{ \frac{1}{4} + \frac{1}{2} }{2}) + f(\frac{\frac{1}{2} + \frac{3}{4} }{2}) + f(\frac{\frac{3}{4} + 1} {2})]$
$M_{4} = \frac{1}{4} [ f(\frac{1}{8}) + f(\frac{3}{8}) + f(\frac{5}{8}) + f(\frac{7}{8})]$

Now, to evaluate your f(x), you need to look at the graph and notice that:
f(x) = x - x³

Therefore:
$M_{4} = \frac{1}{4} [(\frac{1}{8} - (\frac{1}{8})^{3}) + (\frac{3}{8} - (\frac{3}{8})^{3}) + (\frac{5}{8} - (\frac{5}{8})^{3}) + (\frac{7}{8} - (\frac{7}{8})^{3})]$

$M_{4} = \frac{1}{4} [(\frac{1}{8} - \frac{1}{512}) + (\frac{3}{8} - \frac{27}{512}) + (\frac{5}{8} - \frac{125}{512}) + (\frac{7}{8} - \frac{343}{512})]$

M₄ = 1/4 · (2 - 478/512)
= 0.2666

Hence, the area of the region bounded by y = x³ and y = x is approximately 0.267 square units.

6 0

4 years ago

Evaluate A² for A = -3. O-6 O 9 O 6 O-9

Annette [7]

Answer:

A² = 9

Step-by-step explanation:

substitute A = - 3 into A² , that is

A² = (- 3)² = - 3 × - 3 = 9

3 0

2 years ago

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Aleksandr-060686 [28]

Answer: where is the figure tot he right???

Step-by-step explanation:

3 0

3 years ago

You spend $3.40 for a 20 ounce box of cereal what is the rate per ounce

Nataly [62]

3.4/20 divided by 20/20 =.17 The cost per ounce is 17¢

7 0

3 years ago

Write a power represented with a positive base and a positive exponent whose value is less then the base

sasho [114]

Answer:

The question is open ended as i suppose since there are infinitely many possibilities. one possible form of the solution can be $5^{2}$

Step-by-step explanation:

The base in this case is 5 while the exponent is simply the power to which the base is raised in which case it would be 2. Both values are positive and the exponent is less than the base.

6 0

3 years ago