What is the maximum number of possible extreme values for the function f(x)=x^4+x^3-7x^2-x+6
2 answers:
A 4th degree polynomial will have at most 3 extreme values. Since the degree is even, there will be one global extreme, with possible multiplicity. The remainder, if any, will be local extremes that may be coincident with each other and/or the global extreme.
(The number of extremes corresponds to the degree of the derivative, which is 1 less than the degree of the polynomial.)
You might be interested in
The sequences that would map the triangles so as to support both claims are explained below:
<em>Transformation</em> is a process in which the dimensions, size or orientation of a given shape is <em>adjusted</em>. The types are: translation, reflection, rotation and dilation.
Thus;
A. The sequence of transformations that will <u>support</u> Tim's thinking are:
i. <em>Reflection</em> of triangle A <em>about</em> the y-axis.
ii. <em>Reflection</em> of the triangle the <em>second</em> time now about x-axis.
iii. <em>Translation</em> of the triangle two units to the right (i.e towards the x-axis)
These steps would map triangle A unto triangle B supporting Tim's claim.
B. The sequence of transformations that will <u>support</u> Jennifer's claim are:
i. First <em>rotate</em> triangle A by using the origin of the axis as the reference point.
ii. Then <em>translate</em> triangle A two units to the right (i.e towards the x-axis).
Therefore, these steps will map triangle A unto B to support Jennifer's claim.