anonymous
  • anonymous
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).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Any thoughts?
anonymous
  • anonymous
t f t t t t f
anonymous
  • anonymous
I think some of the formatting on these is off.

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anonymous
  • anonymous
For example: 2. If f(x)=e2, then f(x)=2e. What does that mean?
anonymous
  • anonymous
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)
anonymous
  • anonymous
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anonymous
  • anonymous
Well then I disagree with your answers for 7, 6
anonymous
  • anonymous
err 6 and 7 rather.
anonymous
  • anonymous
is 6 not true?
anonymous
  • anonymous
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.
anonymous
  • anonymous
x=0 is an inflection point.
anonymous
  • anonymous
ooh i see
anonymous
  • anonymous
The derivative must be 0 and the concavity must not change signs to have a min/max
anonymous
  • anonymous
yea otherwise it's just an inflection point.
anonymous
  • anonymous
indeed
anonymous
  • anonymous
if the 2nd derivative is >0 then there is a min, right?
anonymous
  • anonymous
I think so yes. The concavity will be positive and not changing signs
anonymous
  • anonymous
yea C.U. has min's Differentiable functions are always continuous - this one false cause they're not always cont. right ?
anonymous
  • anonymous
Differentiable functions are always continuous I think. But the reverse is not true, continuous functions are not always differentiable.
anonymous
  • anonymous
I have to head home. If you have more questions I'll check back later.
anonymous
  • anonymous
alright thanks

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