Question

1. Differentiable functions are always continuous.
2. If f(x)=e2, then f(x)=2e.
3. If f(c)=0 and f(c)0, then f(x) has a local minimum at c.
4. If f(x) and g(x) are increasing on an interval I, then f(x)g(x) is increasing on I.
5. A continuous function on a closed interval always attains a maximum and a minimum value.
6. If f(c)=0, then c is either a local maximum or a local minimum.
7. If f(x)0 for all x in (0,1), then f(x) is decreasing on (0,1).

Answer 1

Any thoughts?

Answer 2

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Answer 3

I think some of the formatting on these is off.

Answer 4

For example:
2. If f(x)=e2, then f(x)=2e.

What does that mean?

Answer 5

it's missing some stuff on my question thou:

2. If f(x)=e2, then f ' (x)=2e.
3. If f ' (c)=0 and f ' ' (c)>0, then f(x) has a local minimum at c.
7. If f ' (x)<0 for all x in (0,1), then f(x) is decreasing on (0,1)

Answer 6

Well then I disagree with your answers for 7, 6

Answer 7

err 6 and 7 rather.

Answer 8

is 6 not true?

Answer 9

No. Look at the derivative of \(x^3\). The derivative equals 0 at x=0, but the function is strictly increasing for all x, so it has no local mins/maxes.

Answer 10

x=0 is an inflection point.

Answer 11

ooh i see

Answer 12

The derivative must be 0 and the concavity must not change signs to have a min/max

Answer 13

yea otherwise it's just an inflection point.

Answer 14

indeed

Answer 15

if the 2nd derivative is >0 then there is a min, right?

Answer 16

I think so yes. The concavity will be positive and not changing signs

Answer 17

yea C.U. has min's

Differentiable functions are always continuous - this one false cause they're not always cont. right ?

Answer 18

Differentiable functions are always continuous I think. But the reverse is not true, continuous functions are not always differentiable.

Answer 19

I have to head home. If you have more questions I'll check back later.

Answer 20

alright
thanks