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.

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?