As topsquark says, "symmetrical with respect to the origin" means it's odd; "touches the x-axis" tells you both y and y' at the indicated point(s). So you'll have three equations with three unknown parameters.View attachment 31245
Can anyone help? I have no idea how to tackle this exercise…
Why don't we consider a constant? ax5+bx3+cx+d. Is it because d=dx0 and x0 is considered as an even powered term?It's symmetric so it's either odd or even. If it were even then the x5 term would spoil that, so it must be odd. Thus all the even power terms are gone and you are looking at ax5+bx3+cx. Can you continue?
-Dan
Do you think the constant term could be symmetric about the origin?Why don't we consider a constant? ax5+bx3+cx+d. Is it because d=dx0 and x0 is considered as an even powered term?
Good point?. If d=0, then f(0)=d. It's no longer at the origin, but at (0,d) instead, because we shifted the function up/down. Thanks.Do you think the constant term could be symmetric about the origin?