abs
What is the differentiability of the function f(x) = $val10 over the interval [-10,10]?
Absolute order
Let $val6: $val7 -> $val7 be the function defined by $val6(x) = $val19. What is the order of differentiability of $val6 ? Instructions/Examples.
- Type 3 if $val6 is differentiable to order 3 but not to order 4.
- Type 0 if $val6 is continuous but not differentiable.
- Type -1 if $val6 is not continuous.
- Type $val8 if $val6 is differentiable to any order.
Continuity of derivative
Let $val6: $val7 -> $val7 be a continuous function. If the derivative $val8(x) exists for any point x
$val7, is the derivative function $val8: $val7 -> $val7 always continuous?
Continuity of derivative II
Let $val8: $val9 -> $val9 be a continuous function. Suppose that the derivative $val10(x) exists for any point x$val11$val9. If furthermore $val16, is the derivative function $val10: $val9 -> $val9 always continuous?
Non-differentiable inverse
The function $val6: $val7 -> $val7 defined by $val6(x) = $val15 is bijective, but there is a point $val8
$val7 such that the inverse function $val6-1(x) is not differentiable on $val8. Find $val8.
Sided order
Let $val6: $val7 -> $val7 be the function defined by $val6(x) = | | $val25 | | si x < $val9 ; |
$val26 | si x $val9 . |
What is the order of differentiability of $val6 ?
Instructions/Examples.
- Type 3 if $val6 is differentiable to order 3 but not to order 4.
- Type 0 if $val6 is continuous but not differentiable.
- Type -1 if $val6 is not continuous.
- Type $val8 if $val6 is differentiable to any order.