Suppose you are working on modeling the adult length of a salamander based on the ambient concentration of oxygen when it undergoes metamorphosis. specifically your are trying to make a function that translates the concentration of dissolved oxygen ,x, in mg/l, into the adult length(x) in cm. through lab experiments and general theory you have deduced that l(8) =15 cm, l′(8) = 0.5 cm/mg/l and l′′(8) = −2 cm/(mg/l)^2.

a) create a second degree taylor polynomial centered at 8 mg/l to predict length from dissolved oxygen concentration. b) use your taylor polynomial to estimate the length when the dissolved oxygen concentration is 7.5 mg/l.