assume f is differentiable and has just one critical point at x3 in pa

Question

Assume f is differentiable and has just one critical point at x=3, In parts (a)-(d) , you are given additional conditions . In each case decide whether x=3 is a local maximum, a local minimum,or neither . You should be able to sketch possible graphs for all four cases. a) f[0] =3 and t [8] = -8 * x=3 is a local maximum . * x=3 is a local minimum * x= 3 is neither a local maximum nor a local minimum. (b) lim f(x)- oo and lim f(x)-oo. * x=3 is a local maximum . * x=3 is a local minimum * x= 3 is neither a local maximum nor a local minimum. c) f(1) = 1, f(2)= 2, f(4) = 3, and f(5) = 4 * x=3 is a local maximum . * x=3 is a local minimum * x= 3 is neither a local maximum nor a local minimum. \mleft(_{}d\mright)f^{\prime}\mleft(2\mright)=-1,f\mleft(3\mright)=1,and\lim _{x\to\infty}f\mleft(x\mright)=3 * x=3 is a local maximum . * x=3 is a local minimum * x= 3 is neither a local maximum nor a local minimum.