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TRUE/FALSE i need to check my work please:(((

1. If f(x) is continuous, then f(x) is differentiable. - true?

2. If f(x) is differentiable, then f() is continuous. - true?

3. The second derivative of a position function is the velocity function. - true?

4. The fourth derivative of a third degree polynomial is zero.??

5. The fourth derivative of sinx is sinx. ??

 Nov 20, 2018
 #1
avatar+16286 
+1

Egad.....that was a long time ago

I THINK:

1 is true

2  not true (I think)

3 Nope  ....FIRST derivative of position is VELOCITY....second is ACCELERATION

4 I THINK so....it would be the derivative of a constant...=0

5 I believe that is true

 Nov 20, 2018
edited by ElectricPavlov  Nov 20, 2018
 #2
avatar+95884 
+1

A long time ago for me too, EP....LOL!!

 

1 False.....the function   y = abs (x)  is continuous, but not differentiable at x = 0

 

2 True....Remember the motto..."Differentability implies Continuity....but Continuity does not imply Differentiability "

 

3 Just as EP said

 

4  Remember that we can take as many non-zero derivatives of a polynomial as its degree

For instance  x^2   ⇒  2x  ⇒ 2   ⇒ 0    [ two non-zero derivatives ]

So....just as EP said !!!

 

5  sin x   ⇒ cos x ⇒ - sin x ⇒ - cos x  ⇒ sin x    ..... true   !!!!

 

 

 

cool cool cool

 Nov 20, 2018
 #3
avatar+16286 
+1

Dang....Quasi-almost-so-close !

ElectricPavlov  Nov 20, 2018

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