Question

:(

Which description could correctly describe the graph of f(x)=−x4+2x3+21x2−62x+40?


A)The function approaches infinity as x approaches positive or negative infinity. The function has a local maximum at (1.47,5.34) and local minima at (−4.72,−764.22) and (3.25,−21.62). The function has zeros at (−7,0), (1,0), (2,0), and (4,0).

b)The function approaches negative infinity as x approaches positive or negative infinity. The function has local maxima at (−3.23,283.11) and (3.26,17.41) and a local minimum at (1.47,−4.08). The function has zeros at (−5,0), (1,0), (2,0), and (4,0).

C)The function that approaches negative infinity as x approaches positive or negative infinity. The function has local maxima at (−5.96,40.04) and (−1.43,3.51) and a local minimum at (−3.11,−8.11). The function has zeros at (−7,0), (−4,0), (−2,0), and (−1,0).

D)The function approaches infinity as x approaches positive or negative infinity. The function has local maxima at (−3.23,283.11) and (3.26,17.41) and a local minimum at (1.47,−4.08). The function has zeros at (−5,0), (1,0), (2,0), and (4,0).

Answer 1

The function approaches negative infinity as x approaches positive or negative infinity. The function has local maxima at (−3.23,283.11) and (3.26,17.41) and a local minimum at (1.47,−4.08). The function has zeros at (−5,0), (1,0), (2,0), and (4,0).

Explanation:

I took the test

Answer 2

b

Explanation:

1. the function will approach negative infinity as x approaches neg/pos infinity because -x^4 (highest power) will result in both ends pointing down. this rules out a and d.

2. skip the Maxima/minima part

3. to test for zeroes, list all possible zeroes using rational zero theorem. then use synthetic division to test out the differing zeroes between b and c.

we find -5 leaves us with remainder of 0, so it is a zero where as -7 leaves us with some remainder that isn't 0, so it is not a zero.

the only option with the function approaching negative infinity with a zero at -5 is b