Question

Find all possible numbers, c, so that y={3x-2c if x is less than or equal to 0}{2x^2+x+5c^2 if x>0} is a continuous function

Answer 1

Hi

Answer 2

Hello!

Answer 3

Have you tried anything yet ?

Answer 4

What do you mean?

Answer 5

I'm not sure how to even start the problem.

Answer 6

Me neither, let's read the problem again.

Answer 7

I can draw the equation out

Answer 8

what does it mean for a function to be "continuous" ?

Answer 9

Is below function continuous ?

Answer 10

No.

Answer 11

why not ?

Answer 12

The graph splits at a number, and it looks as if it has two values for the same place on the graph.

Answer 13

Right, basically we want the function to be smooth

Answer 14

It seems the expression for the function is changing at x = 0 ?

Answer 15

Before x = 0, the expression is 3x-2c
after x = 0, the expression is 2x^2+x+5c^2

Answer 16

For the function to be continuous, we want both those expressions to be same at x = 0

Answer 17

plugin x = 0 and set them equal :

3(0) - 2c = 2(0)^2+0+5c^2

Answer 18

see if you can solve "c"

Answer 19

Okay!

Answer 20

I got 0 and -2/5.

Answer 21

looks good
http://www.wolframalpha.com/input/?i=solve+3(0)+-+2c+%3D+2(0)%5E2%2B0%2B5c%5E2

Answer 22

Awesome! Thank you!

Answer 23

yw!