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