Which is the minimum or maximum value of the given function?
1 answer:
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Answer:
<u>Given function:</u>
- f(x) = (-x + 2)(x + 1)(x +2)
<u>We can rewrite it as:</u>
- f(x) = - (x - 2)(x + 1)(x +2)
<u>Zeros are:</u>
- - (x - 2)(x + 1)(x +2) = 0
- x - 2 = 0 ⇒ x = 2
- x + 1 = 0 ⇒ x = -1
- x + 2 = 0 ⇒ x = -2
As leading coefficient is negative the function is decreasing.
As the function is of degree 3, it is odd.
<u>Considering the above two factors we can define the shape of the graph:</u>
- It is decreasing function with one local minimum and one local maximum.
<em>See the graph and zero's reflected.</em>
