Saddle point (0,0) of the smooth function
x↦{0,if x=0x⋅e−1/x2,otherwise{\displaystyle x\mapsto {\begin{cases}0,&amp;{\text{if }}x=0\\x\cdot \operatorname {e} ^{-1/x^{2}},&amp;{\text{otherwise}}\end{cases}}}
which is a strictly increasing monotonic function. All derivatives of this function in 0 are 0.
Own work
Georg-Johann