sketch the graph of function that meets the stated requirements.

Question

1) Sketch the graph of a function that meets the stated requirements. a) 3 local maxima, 2 local minimum, and no absolute minimum b) two local minima , one local maximum , and five critical numbers

Answer 1

If we have 6 roots with a negative leading coefficient, this will work.

Consider f(x) = -(x-3)(x-2)(x-1)x(x+1)(x+2) and graph from -2.2 to 3.2

(we see that this has no absolute minimum as it goes to - infinity as x goes to infinity and - infinity).

The two local minima and one local maximum insures 3 critical points, and we can get this with four zeroes. Two minima and one max means the leading coefficient is positive. We can make our first and last root have multiplicity 3 to give us 2 extra critical values.

Consider f(x) = x^3*(x-1)*(x-2)*(x-3)^3 and graph from -.5 to 3.5