If f(x) is continuous and differentiable and f(x) = ... then b?
f(x) =
{ax^4 + 5x, x< or = 2
{bx^2 - 3x, x> 2,
then b = ?
Help pls

- anonymous

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- myininaya

1st set these two expressions equal to each other: \[\lim_{x \rightarrow 2^-}f(x)=\lim_{x \rightarrow 2^+}f(x)\]

- myininaya

2nd set these two expressions equal to each other:
\[\lim_{x \rightarrow 2^-}f'(x)=\lim_{x \rightarrow 2^+}f'(x)\]

- anonymous

What should I do after that? Add those two equations together?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- myininaya

You will have a system of equations to solve just like from algebra class.

- anonymous

Well I got, 4a - 10 = 4b - 6 and then -32 + 5 = 4b - 3. Is that correct?

- myininaya

The first equation on the left hand side you have 4a-10
I think it should be 16a+10.
What happen to a in the second expression?

- myininaya

I mean equation err

- anonymous

oops you are right.

- myininaya

\[a(2)^4+5(2)=b(2)^2-3(2) \text{ first equation }\]

- myininaya

\[4a(2)^3+5=2b(2)-3 \text{ second equation }\]

- anonymous

Wait isn't it a(-2)^4 + 5 (-2) since the limit is coming from the left side?

- myininaya

It isn't approaching -2. It is approaching 2.

- myininaya

You have the left is just approaching 2 from the left.
You have the right is just approaching 2 from the right.
Either way they are both still approaching 2 and not some other number.

- anonymous

Ahh ok I got it :) After I get these 2 equations then what should I do afterward?

- myininaya

Have you ever solved a system of two linear equations?

- anonymous

Yes, like 4 years ago haha.

- anonymous

16a + 10
4b - 6
32a + 5
4b - 3 ( Can't I just substitute it and then solve it) ?

- myininaya

You can put them both in ax+by=c form if you want.
Like if we had something like 2x+3y=1
-2x+3y=1
This system is already set up for elimination. Add the equations together and solve for y first would be my strategy.
6y=2
y=2/6=1/3
Then plug into one of the other equations and solve for x.

- myininaya

Or this system:
3x-6y=2
x+y=2
This one isn't set up for elimination. But you could multiply the bottom equation by -3 so we would have it setup for elmination.
3x-6y=2
-3x-3y=-6
----------------add
-9y=-4
y=4/9
and then so on to find x.

- myininaya

\[a(2)^4+5(2)=b(2)^2-3(2) \text{ first equation }\]
\[16a+10=4b-6\]
\[16a-4b=-16 \text{ rewrote the equation 1} \]

- myininaya

Do you think you can rewrite equation 2 in that form?

- anonymous

32a - 4b = -8 ( 2nd equation right) right?

- myininaya

looks good

- myininaya

So we have
16a-4b=-16
32a-4b=-8

- myininaya

If we multiply the second or even the first (just not both of them) by -1, then we can set this up for elimination method.

- myininaya

I'm trying to eliminate b. (you could go for a but I prefer working with smaller numbers)

- myininaya

So
-16a+4b=16
32a-4b=-8
----------------add the equations together and what do we get?

- anonymous

I got the final answer of 6 for b. Is that right?

- anonymous

and .5 for a

- myininaya

yep. good job.

- anonymous

yayyy, you should just be my tutor haha. Thank you so much :D

- myininaya

np

Looking for something else?

Not the answer you are looking for? Search for more explanations.