please help with this calculus question

[needsomehelpin]

Suppose a function satisfies f(0) = 1 and f(2) = -1

What can we say about the roots of the functions between 0 and 2

 

[pka]

Suppose a function satisfies f(0) = 1 and f(2) = -1
What can we say about the roots of the functions between 0 and 2

\(\displaystyle \L
f(x) = \left\{ \begin{array}{l}
x^2 + 1,\quad x \le 1 \\
- 1,\quad ,1 < x \\
\end{array} \right.\)
NOTHING? This function has no roots.

 

[needsomehelpin]

ok thanks but can you explain that because what you wrote means nothing to me i have no clue what it means

 

[stapel]

ok thanks but can you explain that because what you wrote means nothing to me i have no clue what it means

Which part do you not understand? "Function"? "Roots"? "Satisfies"? Something else?

Please be specific. Thank you.

Eliz.

 

[soroban]

Hello, needsomehelpin!

Surely, there's more information . . .

Suppose a function satisfies \(\displaystyle f(0)\,=\,1\) and \(\displaystyle f(2)\,=\,-1\)
What can we say about the roots of the functions between 0 and 2

I'll take a flying guess at what the original problem said . . .

Suppose a continuous function satisfies \(\displaystyle f(0)\,=\,1\) and \(\displaystyle f(2)\,=\,-1\) . . .

          |
          *(0,1)
          |
    - - - + - - - - -
          |
          |       *(2,-1)
          |

If the function is continuous, its graph connects (0,1) and (2,1).
\(\displaystyle \;\;\)Hence, it will cross the x-axis (at least once) between \(\displaystyle x = 0\) and \(\displaystyle x = 2.\)

Therefore, the function has at least one root on the inverval \(\displaystyle (0,\,2).\)

 

[stapel]

If the function is continuous....

But if it isn't continuous, then, as the other tutor mentioned, we can draw no conclusions.

Eliz.