Question

so maybe you can help me with this problem also:

For what value of the constant c is the function f continuous on (−infinity, infinity)?
f(x) = cx2 + 5x if x < 6
x3 − cx if x ≥ 6


I dont understand the steps and finding this answer . the whole infinity thing throws me off

Answer 1

In this, the limits at infinity simply mean that as far as you go left or right the function is always continuous. To make that true also, the two halves of the piecewise function would have to be equal at x=6. So you just set \[cx^2+5x = x^3+6\] and then put in 6 for x and solve for c.

Answer 2

it has to do with the function meeting up at x=6. just like @jeherohaku wrote.

Answer 3

so why isn't the rewritten equation:
\[cx ^{2}+5x=x ^{3} +c6\]

Answer 4

probably a typo

Answer 5

Your rewritten equation should be \[c(6)^2+5(6)=(6)^3+6\] so that you only have one unknown, the c.

Answer 6

oh okay,
im still confused though

Answer 7

no... that's not right. you have to include the c in both places.

Answer 8

so what exactly happened to the other c

Answer 9

then combine like terms and solve for c.

Answer 10

OH yeah whoops i had a typo. sorry guys.

Answer 11

\[c(6)^{2} +5(6) = (6)^3 -c(6) \text{ solve for c.} \]

Answer 12

Did you get a value for c?

Answer 13

4.429 and its saying that it is wrong

Answer 14

im doing practice problems on the computer

Answer 15

try it as a fraction... or mixed number.

Answer 16

you've got the right number (I believe) just maybe not the right form. if it's decimal to 3 places, i get the same thing. but they may want a fraction (improper) or mixed number.

Answer 17

i did. its not working as long as i got the answer correct Im okay. i just wanted a understanding of what was going on. my professor sometimes flies over lessons and missing one thing throws me off. i try reading out the textbook but Im more of a visual hands on person. however you guys really helped i appreciate your patience with me. Thank You

Answer 18

what was the fraction you got?

Answer 19

or mixed...

Answer 20

31/7

Answer 21

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Answer 22

perfect, I got that and it works so something must be up with the answer sheet or program