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. ??

Guest 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

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 !!!!

CPhill Nov 20, 2018