Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of f are shown in the graph.
I really need help with this one but I can't post the graph.
wherever it crosses the x axis is a zero so
(x - xcrossing ) is a factor
If it gets near the x axis but goes horizontal and veers away again, that is a complex root pair.
like
y = x^2 + 2 x + 4
zeros at
x = [ -2 +/-sqrt (4 - 16)]/2
x = -1 +/- (1/2)sqrt (-12)
= -1 +/- i sqrt 3
where would that be horizontal (extrema)?
0 = 2x + 2
x = -1 at extrema (sure enough)
if it goes big +y for both big plus and minus x, then the first term is a x^even power
if it is big minus for -x and big Plus for +x (or vice versa for - coefficient)then first term is x^odd power.
it really helped
No worries, I can still help you analyze and interpret the graph without actually seeing it. Just describe the features of the graph as best as you can, and I'll guide you through the process of answering the questions. For reference, here are the questions you mentioned:
1. How many local extrema does the polynomial function f have?
2. Are the local extrema maxima or minima?
Please describe the key characteristics of the graph, such as the shape, direction, and any notable points or behaviors.