Help with geometry please !

The graph of the continuous function g, the derivative of the function f, is shown above. The function g is piecewise linear for

4vir4ik [10]

A) $g=f'$ is continuous, so $f$ is also continuous. This means if we were to integrate $g$ , the same constant of integration would apply across its entire domain. Over $0$ , we have $g(x)=2x$ . This means that

$f_{0$

For $f$ to be continuous, we need the limit as $x\to1^-$ to match $f(1)=3$ . This means we must have

$\displaystyle\lim_{x\to1}x^2+C=1+C=3\implies C=2$

Now, over $x$ , we have $g(x)=-3$ , so $f_{x$ , which means $f(-5)=17$ .

b) Integrating over [1, 3] is easy; it's just the area of a 2x2 square. So,

$\displaystyle\int_1^6g(x)=4+\int_3^62(x-4)^2\,\mathrm dx=4+6=10$

c) $f$ is increasing when $f'=g>0$ , and concave upward when $f''=g'>0$ , i.e. when $g$ is also increasing.

We have $g>0$ over the intervals $0$ and $x>4$ . We can additionally see that $g'>0$ only on $0$ and $x>4$ .

d) Inflection points occur when $f''=g'=0$ , and at such a point, to either side the sign of the second derivative $f''=g'$ changes. We see this happening at $x=4$ , for which $g'=0$ , and to the left of $x=4$ we have $g$ decreasing, then increasing along the other side.

We also have $g'=0$ along the interval $-1$ , but even if we were to allow an entire interval as a "site of inflection", we can see that $g'>0$ to either side, so concavity would not change.

5 0

3 years ago

Loli-Land Candy Store sells a 12 ounce bag of 60 mints. What is the number of mints per ounce?

Vsevolod [243]

5 because you have to divide 60 by 12.

6 0

3 years ago

More is coming but help help help #10 points

vovangra [49]

Answer:

Its the last one

Step-by-step explanation:

The angle R is supposed to be the letter in the middle which is known as the vertex in an angle,It leads to the angle in degrees forming a proper angle.

It not much information because its hard to explain but,hope this helps!!!.

6 0

3 years ago

The formula for the surface area of a cylinder with radius r and height h is at times twice the product of the

MrMuchimi

Answer:

<em> $2\pi \: rh + 2\pi {r}^{2} = 2(t \times {r}^{2} )$ </em>

Step-by-step explanation:

The TSA of the cylinder

$2\pi \: rh + 2\pi {r}^{2}$

In Mathematics, 'is' is =

Twice means 2( )

Product means ×

So we have

$2\pi \: rh + 2\pi {r}^{2} = 2(t \times {r}^{2} )$

as the answer.

6 0

3 years ago

You make picture frames to sell at the flea market; you spent $46 on supplies and you want to sell the frames for $8.50 each. Ho

BARSIC [14]

<h3>Answer: 6 Frames</h3>

Before we start, let us figure out what profit means?

Profit is the money you make.

Note: Income is the money you receive, and expenses are the money you spend on your business.

If you sold five frames, you would make: (8.50 x 5 = $42.50)

Note: $42.50 <u>is not</u> greater than your expenses, so you haven't make any profit yet.

If you sold six frames, you would make: (8.50 x 6 = $51.00)

Note: $51.00 <u>is</u> greater than your expenses, so you made some profit.

<h3>Additional Information</h3>

To find the money you made or your profit, simply subtract the money you received from your expenses.

$51.00 - $46.00 = $5.00

You only made <u>$5.00</u>, but to make a larger profit, you have to sell more frames.

<h3>Conclusion</h3>

I hope my explanation provided excellent aid. Oh, and you're welcome.

3 0

3 years ago