Math

h.w16.docx

 Give an example of a polynomial (x) of degree 5 for which = 1 is a critical number but not a local minimum, nor a local maximum. (Hint: An example of a polynomial of degree is (x) = (x-a)^k .

 (2--5) Determine the intervals on which the function is decreasing and increasing and then find local minima and maxima. (x) = (x-2)(x+3)

 (x) = (x+1)(x-2)(x+3)

 (x) = x e^(-x)

 (x) = x^x defined on the interval 0, infinity) .

 Let (x) = cos x+2 cos^2 x defined for i/2 < x < pi . Determine the local extrema and inflection points.

 [Please discuss but no need to submit.] The graph of is located below the X-axis except for one point where it touches the -axis at . What can you say about the function ?

Hint: What are the intervals of monotonicity of ? Does have a crictical point?

Does the function whose derivative is illustrated in the graph below satisfy the above conditions?