math

h.w14.docx

 For the function (x) sketched below, find for what does the function (x) reach

(a) the absolute maximum value,

(b) the absolute minimum value,

(d) What is the absolute minimum value of (x) ?

ttp://calculus.sfsu.edu/latexrender/pictures/236ef7756ad5a90ecad8d71188517820.png

 For the function (x) sketched above, find

(a) values for which '(c) = 0 ,

(b) values for which '(c) does not exist,

(d) Does the function reach every value between its absolute minimum value and its absolute maximum value?

Problems 3--5. The following functions are defined for all . Find the critical numbers if they exist. Explain in a sentance how you do it.

 (x) = x .

 (x) = x^3+3 x^2-24 x

 (x) = |2 x+3|

ttp://calculus.sfsu.edu/latexrender/pictures/7777af725016fe8171aa88137d5a661f.png

 Find critical numbers for (t) = root(t)(1-t) where > 0 . What will you do first?

 Find the maximum and minimum values of (x) = 3 x+1 defined on the interval 3,6] .

 Find the maximum and minimum values of (x) = x^2+4 defined on the interval -2,6] .

 Find the maximum and minimum values of (x) = sin (2x)+cos (2x) on the interval -pi/4, pi/2] . Then graph the function to check your answers.