Find all relative extrema of the function. use the second derivative test where applicable. (if an answer does not exist, enter
dne.) f(x) = x2 + 3x − 1
1 answer:
The given quadratic describes a parabola that opens upward. Its one absolute extreme is a minimum that is found at x = -3/2. The value of the function there is
(-3/2 +3)(-3/2) -1 = -13/4
The one relative extreme is a minimum at (-1.5, -3.25).
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For the parabola described by ax² +bx +c, the vertex (extreme) is found where
x = -b/(2a)
Here, that is x=-3/(2·1) = -3/2.
(-3/2 +3)(-3/2) -1 = -13/4
The one relative extreme is a minimum at (-1.5, -3.25).
_____
For the parabola described by ax² +bx +c, the vertex (extreme) is found where
x = -b/(2a)
Here, that is x=-3/(2·1) = -3/2.
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Answer:
{4}
Step-by-step explanation:
It is helpful to let a calculator or spreadsheet perform the function evaluations for you. The two functions have the same value only for x=4 in the domain.
f(4) = 13 = g(4)
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The functions also have the same value for x=-2, but that is not in the domain given.
