Question

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Answer 1

f is continuous on [-5,5] such that f(-5)=-10 and f(5)=10 decide which of the following statements are true and which are flase

Answer 2

F is an even function

Answer 3

That's not necessarily true, since for an even function, f(x)=f(-x), and in this case, f(5) does not equal f(-5).

Answer 4

Sorry, I meant not true at all - it can't be even.

Answer 5

So is that neither

Answer 6

f'(c)=2 for at least one c between -5 and 5

Answer 7

There's a theorem, the Mean Value Theorem, which guarantees that if a function is continuous and has an average slope m on an interval, then its derivative will be m at some point. So true.

Answer 8

f(c)=9 same question above

Answer 9

That's not necessarily true - the Mean Value Theorem doesn't make any guarantees about the value of the function at any point.

Answer 10

you really don't need the Mean Value Theorem, it's a rather intuitive question
If you think about it like this, obviously it's going to be 2 somewhere

Answer 11

Not always immediately clear, theorems can ease the mind.