Answer :
Final answer:
To find the x-values where f(x) has a relative minimum, we need to find the critical points by setting the derivative of f(x) equal to zero. Solving the equation yields x = 1 as the x-value where f(x) has a relative minimum.
Explanation:
To find all x-values where f(x) has a relative minimum, we need to first find the critical points of the function. These are the points where the derivative of the function is equal to zero. Let's calculate the derivative of f(x) and set it equal to zero:
First derivative of f(x): f'(x) = 10x^4 - 100x^3 + 360x^2 - 560x + 320
Setting f'(x) = 0 and solving for x:
10x^4 - 100x^3 + 360x^2 - 560x + 320 = 0
We can factor the equation to find the values of x:
x = 1
Therefore, the x-value where f(x) has a relative minimum is x = 1.
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