What is angle 2? I don’t know this please help me

Consider the equation below. f(x) = 2x3 + 3x2 − 336x (a) Find the interval on which f is increasing. (Enter your answer in inter

Vaselesa [24]

We have been given a function $f(x)=2x^3+3x^2-336x$ . We are asked to find the interval on which function is increasing and decreasing.

(a). First of all, we will find the critical points of function by equating derivative with 0.

$f'(x)=2(3)x^{2}+3(2)x^1-336$

$f'(x)=6x^{2}+6x-336$

$6x^{2}+6x-336=0$

$x^{2}+x-56=0$

$x^{2}+8x-7x-56=0$

$(x+8)-7(x+8)=0$

$(x+8)(x-7)=0$

$x=-8,x=7$

So $x=-8,7$ are critical points and these will divide our function in 3 intervals $(-\infty,-8)U(-8,7)U(7,\infty)$ .

Now we will find derivative over each interval as:

$f'(x)=(x+8)(x-7)$

$f'(-9)=(-9+8)(-9-7)=(-1)(-16)=16$

Since $f'(9)>0$ , therefore, function is increasing on interval $(-\infty,-8)$ .

$f'(x)=(x+8)(x-7)$

$f'(1)=(1+8)(1-7)=(9)(-6)=-54$

Since $f'(1)$ , therefore, function is decreasing on interval $(-8,7)$ .

Let us check for the derivative at $x=8$ .

$f'(x)=(x+8)(x-7)$

$f'(8)=(8+8)(8-7)=(16)(1)=16$

Since $f'(8)>0$ , therefore, function is increasing on interval $(7,\infty)$ .

(b) Since $x=-8,7$ are critical points, so these will be either a maximum or minimum.

Let us find values of f(x) on these two points.

$f(-8)=2(-8)^3+3(-8)^2-336(-8)$

$f(-8)=1856$

$f(7)=2(7)^3+3(7)^2-336(7)$

$f(7)=-1519$

Therefore, $(-8,1856)$ is a local maximum and $(7,-1519)$ is a local minimum.

(c) To find inflection points, we need to check where 2nd derivative is equal to 0.

Let us find 2nd derivative.

$f''(x)=6(2)x^{1}+6$

$f''(x)=12x+6$

$12x+6=0$

$12x=-6$

$\frac{12x}{12}=-\frac{6}{12}$

$x=-\frac{1}{2}$

Therefore, $x=-\frac{1}{2}$ is an inflection point of given function.

3 0

3 years ago

Evaluate each expression <br> 8-(-5)-3

Vesnalui [34]

<h3>Answer:</h3>

$\large\boxed{10}$

<h3>Step-by-step explanation:</h3>

In this question, we're evaluating the given expression.

The given expression is:

$8-(-5)-3$

We would simply solve the equation until we reach our final answer.

Solve:

$8-(-5)-3\\\\\text{The "-(-" will turn to a plus sign}\,\,\\\\8+5-3\\\\\text{Add 8 and 5}\\\\13-3\\\\\text{Finish off by subtracting}\\\\10$

A friendly reminder is when you see something like "-(-", you would turn it into a plus sign.

When you're done solving, you should get 10.

This means that 10 would be your final answer.

<h3>I hope this helped you out.</h3><h3>Good luck on your academics.</h3><h3>Have a fantastic day!</h3>

5 0

4 years ago

Read 2 more answers

What is 3/3 plus 4 6/4?

Kitty [74]

Answer:

78/12 or 6 1/2

6 0

3 years ago

I don’t 100% remember how to turn this into a standard problem.. could someone help me really quick?

marin [14]

Standard form is ax^2+bx+c=0

First evaluate the exponent and expand (foil).
y= 3(x^2-4x+4)+1

Then distribute the 3
y= 3x^2-12x+12+1

Combine like terms
y=3x^2-12x+13

Final answer: 3x^2-12x+13=0

6 0

3 years ago

Find the area of the shape.

-BARSIC- [3]

Answer:

12.56

Step-by-step explanation:

area of a circle is A=πr^2

radius is 2

a= 3.14 (2)^2

=3.14 x 4

=12.56

7 0

2 years ago