Using MATLAB 1. Consider the function f(t) = t^6 4t^4 2t^3 + 3t^2 + 2t on the in

Question

Using MATLAB

1. Consider the function f(t) = t^6 4t^4 2t^3 + 3t^2 + 2t on the interval 1.5 , 2.5.

(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 1.5 , 2.5 . 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?

Explanation / Answer

1. x=-1.5:0.01:2.5;

y=x.^6-4*x.^4-2*x.^3+3*x.^2+2*x;

plot(x,y);

2. 3 local extrema from looking at the graph

There are still 3 extrema even after axis command

axis([-1.5 2.5 0 inf])

3. The derivative of f is 6t^5-16t^3-6t^2+6t+2

t=-1.5:0.01:2.5;
>> y=6*t.^5-16*t.^3-6*t.^2+6*t+2;
>> plot(x,y)
>> axis([-1.5 2.5 0 inf])

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