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Hollysmoke
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Is it possible to have 2 global minimums? I'm just having trouble determining whether this quartic has minimums or not =/
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Hollysmoke said:Is it possible to have 2 global minimums? I'm just having trouble determining whether this quartic has minimums or not =/
NateTG said:No. There is only one global minimum, however, a function can be minimal in more than one place.
For example, the function:
f(x)=0
is minimal everywhere.
Hollysmoke said:So there are no minimums in this case?
Hollysmoke said:Becaue when I try to calculate it, the 3 critical numbers I get are 2,-2, and 0. But if I sub in 2 or -2, I get 6, which doesn't seem right...
Beam me down said:But isn't the definition of the minimum (not at a domain endpoint) that:...
Curve sketching is a process of visually representing a function by plotting its key features such as intercepts, extrema, and asymptotes. It helps in understanding the behavior and characteristics of a function.
A quartic function is a polynomial function of degree four. It is represented by the general form f(x) = ax^4 + bx^3 + cx^2 + dx + e, where a, b, c, d, and e are coefficients. It can have up to four real roots and four turning points.
To identify multiple global minimums in a quartic function, you need to find the points where the function changes direction from decreasing to increasing. These points are the local minimums, and the lowest among them is the global minimum. In a quartic function, there can be up to four local minimums, and the number of global minimums can be either one or two.
The first derivative of a function represents its rate of change at a given point. It can help in identifying the critical points, which are the points where the function changes from increasing to decreasing or vice versa. These points can be used to determine the local extrema and the concavity of the function, which are crucial in curve sketching.
No, a quartic function can have a maximum of two global minimums. This is because a quartic function is a polynomial of degree four and can have a maximum of four real roots. As the function approaches infinity, the graph becomes increasingly flat, and therefore, there can only be a maximum of two global minimums.