Question

Math

Posted 5 months ago

```
The derivative of a function $f$ is given by $f^{\prime}(x)=x^{4}-x^{3}-2 x^{2}+4 x-2$.
Where does the graph of $f$ have a relative minimum? Use a graphing calculator.
Choose 1 answer:
(A) $x=-2$
(B) $x=-1.769$
(C) $x=-1.067$
(D) $x=1$
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 2

The derivative $f'(x)$ is given by $f'(x) = x^4 - x^3 - 2x^2 + 4x - 2$

step 3

According to the asksia-ll calculator, the function $f$ has a relative minimum at $x \approx -1.06659$

step 4

Comparing this result with the given options, the closest value to $x \approx -1.06659$ is (C) $x = -1.067$

C

Key Concept

Relative Minimum

Explanation

The relative minimum of a function occurs at a critical point where the derivative changes from negative to positive, indicating a trough in the graph of the function.

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