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#### Guest

##### Guest

a) find all x values where it is increasing and all values where it is decreasing ---> derivative is e^(-2x)-2xe^(2x)

b) give absolut min and max

2. Let f be the function defined by f(x) = x^3+ax²+bx+c and having the following properties

(i) graph has a point of inflection at (0,2)

(ii) mean value of f(x) on [0,2] is -3

a) determine a, b and c

b) determine the value of x that satisfies the conclusion of the mean value therorem for f on [0,3]

3. position func x(t)=sin(pi*t²)

a) velocity ---> cos(pi*t²)(2pi*t)

b) Acceleration ---> 2pi[cos(pi*t²)-tsin(pi*t²)]

c) Wheat values of t does the particle change direction ---> sign chart, decreasing [-1,0) increasing (0,1] so t=0 is where is changes direction

d) find what values for t for which it is moving to the left