Indledning
A term is either a number, variableor variables multiplied together.
The terms areseparated from each other by + or - hence x+4 consists of 2 terms.A polynomial means “many terms” and the general form of a nth degree polynomial is P(x)=ax^n+ax^(n-1)+ax^(n-2)....ax^(n-n (0)).
Indholdsfortegnelse
The general form of a polynomial and what a term consists of.
The shape of the graphs of a 2nd degree polynomial from the coefficients, a, b, and c – and the discriminant, d
Analyze the following cubic function:f(x)=-x^3-11x^2-14x+80
- Newton-Raphson:
- Following changes are marked in red
- The extrema
- The sign variation of the function and monotonicity
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Uddrag
The function f(x)=-x^3-11x^2-14x+80that we must analyze has the highest power of 3 and is therefore a 3rd degree polynomial or a cubic function.
It consists of 4 terms and when differentiatingusing the power rule /nxn-1/ f 1 (x)= -3x3-1 -11*2x2-1 -14 we getf^1 (x)=-3x^2-22x-14.When sketching we can see that the graph has two turning points.
The first turning point is a local minimum, as the signs change from negative to positive andthe second turning point is a local maximum, as the signs change from maximum to minimum.
We also see that the horizontal extent of the graph is the whole real number line and the same applies to the vertical extent of the graph, therefore bothits domain and range go from -∞ to ∞, (D∈R and R∈R)
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