Can someone help me

I WILL GIVE BRAINLIEST TO WHOEVER IS CORRECT!!!!!!

melisa1 [442]

Match the whole number and the bottom fraction number and gets u answer!

3 0

3 years ago

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:

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

So

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

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

4 years ago

PLEASE HELP ME ASAP!!!!!Sarah rolled a number cube 30 times and recorded the results. She found that she rolled an even number 1

Law Incorporation [45]

Answer:

B,

c,

B,

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Mang Nathaniel is selling two kinds of vinegar. Silver duck is priced at Php

Vladimir [108]

Answer:

Reyna Puti sold = 20 bottles

Step-by-step explanation:

Silver duck = Php 10 per bottle

Reyna Puti = Php 15 per bottle

Silver duck sold = 30 bottles

Reyna Puti sold = x bottles

Total sales = Php 600.00

Total = cost of Silver duck * number sold + cost of Reyna Puti * number sold

600 = 10 * 30 + 15 * x

600 = 300 + 15x

600 - 300 = 15x

300 = 15x

x = 300/15

x = 20 bottles

Reyna Puti sold = 20 bottles

3 0

3 years ago

Help please V/5 = 3/7 v=

Serggg [28]

Answer:

v = 15/7, or 2.14

Step-by-step explanation:

Find a common denominator, or multiply both denominators by each other, and well as the numerator.

v/5 = 3/7 can be written as 7v/35 = 15/35

multiplying both sides with 35, we are left with 7v = 15

v = 15/7, or 2.14

8 0

3 years ago

Read 2 more answers