answers a to h A continuous function f is defined on [0, 6] and its graph is giv

Question

answers a to h

A continuous function f is defined on [0, 6] and its graph is given below. If , for 0 x 6, answer the following questions. Is g(0) negative, positive or zero? Is g(6) negative, positive or zero? Find all x where g'(x) = 0. Determine the intervals where g is increasing and where decreasing. Does g have an absolute maximum and an absolute minimum? If there are absolute extreme values for g determine the x-coordinates of the place(s) where they occur and explain your answer. Determine where the graph of g is concave up and where concave down. Sketch a possible graph of g incorporating the properties discussed in (a) - (f) above. If h(x) = , find h'(4).

Explanation / Answer

a) g(0)=0
   g(6)= -ve
b)x=2,5
c)x=[0,5] decreasing.....x=[5,6] increasing
d) yes g has absolute minimum
e) g is minimum at x=5 because f(x)=d/dx(g)
f)x=[0,2] concave down for allother x concave up
h)h'(x)=g'(rootx)/2*root(x)= 0 since g'(2)=0

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