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

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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
+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
+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   !!!!   Nov 20, 2018
#3
+1

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

ElectricPavlov  Nov 20, 2018