Consider the function f(t) = t 6 4t 4 2t 3 + 3t 2 + 2t on the interval 3 2 , 5 2 .

(a) Graph the function on the given interval.

(b) Determine how many local extrema the function has. In particular, produce a separate graph which is zoomed in closer to x = 1 to confirm your result using the axis command.

(c) Find the derivative of f and graph it on the interval 3 2 , 5 2 . Using this graph to identify appropriate guess values, use fzero to find the approximate locations of each local extremum to at least 6 decimal places.

(d) Graph f 00 on the interval 1.2 t 0.8. How does the graph establish that x = 1 is, in fact, an inflection point of f? 2.

Use matlab code!