Use the following partial graph of a polynomial function, with a local maximum at x=-4 and a local minimum at x=2

Question

Compare f(1.9) and f(2.1) with f(2)

Answer 1

if a local minimum is when x=2, then f(2) is a local minimum

and f(1.9) and f(2.1) are slightly more than f(2)

f(1.9)>f(2)

f(2.1)>f(2)

if a local max is at x=-4

the polynomial is at least cubic, y=f(x)=ax^3 +bx^2 +cx + d

if cubic then

y' = 0 = f(-4)= f(2)

= 8a +4b+2c

= -64a +16b-4c

the max and min points also give you some info about the 2nd derivatives f"(2) and f"(-4), their signs