Question 175746This question is from textbook Algebra 2
: How do I graph this polynomial function? f(x)=x^4 - 2x^3 - 3x^2 + 5x + 2.
Thank you very much.
This question is from textbook Algebra 2
Found 2 solutions by josmiceli, nabla:
Answer by josmiceli(19441)   (Show Source):
Answer by nabla(475)  (Show Source):
You can put this solution on YOUR website! 1) Factor to f(x)=(-2 + x) (-1 - 3 x + x^3)
2) The first evident, real root will be x=2.
3) It should be noted that this will "eventually" resemble a parabola. Moreover, our interest will be around x=2.
4) Techniques of calculus will give us concavity, max, min, inflection.
f'(x)=4x^3-6x^2-6x+5=0 gives criticals of
x -> -1.05274
x -> 0.611731
x -> 1.94101
If you test outside the intervals you will note changes in direction of the slope this is indicative of extrema.
Thus: x=-1.05274 is local minimum
x=0.611731 is local maximum
x=1.94101 is local minimum
Concavity [not entirely necessary]:
f''(x)=12x^2-12x-6=0
gives
x -> -0.366025
x -> 1.36603
Testing intervals again you will find CU on (-inf, -0.366025), CD on (-0.366025, 1.36603), then CU on (1.36603, inf).
This is certainly enough information to produce the following graph:
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