Let  fxbe a polynomial of degree 5 such that  x=±1are its critical points. If  limx→02+fxx3=4, then which one of the following is not true?

Let fx=ax5+bx4+cx3.  Thenlimx→02+ax5+bx4+cx3x3=4⇒2+c=4⇒c=2Also f'x=5ax4+4bx3+6x2=x25ax2+4bx+6.Since x=±1 are points of extremum, we havef'1=0 and f'−1=0⇒5a+4b+6=0 and 5a−4b+6=0⇒b=0,a=−65⇒fx=−65x5+2x3⇒ f'x=−6x4+6x2 ⇒f''x=-24x3+12x Now f''-1=12>0 and f''1=-12<0⇒minimum at x = -1 and maximum at x = 1