[fxj]

just tried this: take the graph of the functions x^n and exp(x) how many points of intersection do they have?

chatgpt gave me the wrong answer, it claimed 2 points of intersection, but for n=4 there are 3 as one can easily derive. one for negative x and 2 points for positive x because exp(x) is growing faster than x^4.

then i corrected it and said 3 points of intersection. it said yes and gaev me the 3 points. then i said no there are 4 points of intersection and it again explained to me that there are 2 points of intersection. which is wrong.

then i asked it how many points of intersection for n=e and it said: zero

well, exp(x)=x^e for x=e, isnt it?