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4 years ago

11

Mathematics

1 answer:

aalyn [17]4 years ago

5 0

Answer:

rational, integer

Step-by-step explanation:

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Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x3 − 6x2 − 15x + 2 (a) Find the interval on which

Burka [1]

Answer:

a) $(-\infty, -1) \cup (5, \infty)$

b) $(-1,5)$

Step-by-step explanation:

The first step to solve this question is finding the roots of the derivative of x.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$f(x) = x^{3} - 6x^{2} - 15x + 2$

$f'(x) = 3x^{2} - 12x - 15$

Finding the roots:

$3x^{2} - 12x - 15 = 0$

Simplifying by -3

$x^{2} - 4x - 5 = 0$

So $a = 1, b = -4, c = -5$

Then

$\bigtriangleup = (-4)^{2} - 4*1*(-5) = 36$

$x_{1} = \frac{-(-4) + \sqrt{36}}{2} = 5$

$x_{2} = \frac{-(-4) - \sqrt{36}}{2} = -1$

So the function can be divided in three intervals.

They are:

Less than -1

Between -1 and 5

Higher than 5

In which it increases and which it decreases?

Less than -1

Lets find the derivative in a point in this interval, for example, -2

$f'(x) = 3x^{2} - 12x - 15$

$f'(-2) = 3*(-2)^{2} - 12*(-2) - 15 = 21$

Positive.

So in the interval of $(-\infty, -1)$ , the function increases.

Between -1 and 5

Will choose 0.

$f'(x) = 3x^{2} - 12x - 15$

$f'(0) = 3*(0)^{2} - 12*(0) - 15 = -15$

Negative.

So in the interval of $(-1,5)$ , the function decreases.

Higher than 5

Will choose 6.

$f'(x) = 3x^{2} - 12x - 15$

$f'(6) = 3*(6)^{2} - 12*(6) - 15 = 21$

Positive

So in the interval of $(5, \infty)$ , the function increases.

(a) Find the interval on which f is increasing.

Using interval notation

$(-\infty, -1) \cup (5, \infty)$

b) Find the interval on which f is decreasing.

$(-1,5)$

5 0

3 years ago

What is the simplified expression for -3(2x-7)+2y+ 2(x+y)?

PilotLPTM [1.2K]

Answer:

-4x+4y+21

Step-by-step explanation:

-3(2x-7)+2y+2(x+y)

-6x+21+2y+2x+2y

-4x+21+4y

-4x+4y+21

Expanded and simplified :)

8 0

3 years ago

Use an algebraic equation to find the measures of the two angles described below. Begin by letting x represent the degree measur

faltersainse [42]

Answer:

i am not sure

Step-by-step explanation:

7 0

3 years ago

A scale drawing shows a circular fountain with a diameter of 12 units. The actual fountain has a diameter of 60 feet. Select all

EleoNora [17]

Answer:i think its 70 if im wrong im very sorry

Step-by-step explanation:

5 0

3 years ago

Can someone help me with this question?

meriva

Whenever you have __% more of something and want to find the new value, first convert the percent to a decimal. Then multiply the original value by (1.00+that decimal).

You have 6480 kg of sugar. 75%=0.75. If you want 75% more sugar, you would want 6480*(1.00+0.75) = 6480*(1.75) = 11,340 kg of sugar.

5 0

3 years ago