Given the numerical values shown, find approximate values for the derivative of

Question

Given the numerical values shown, find approximate values for the derivative of f (x) at each of the X-values given. Please estimate the derivative by using averages. Where is the rate of change of f (X) positive? The rate of change or f(x) is positive for lessthanorequalto X lessthanorequalto Where is the rate of change of f (x) negative? The rate of change of f (x) i$ negative for lessthanorequalto X lessthanorequalto Where does the rate of change of f (x) seem to be greatest? The rate of change is greatest at about x =

Explanation / Answer

as we know f'(x) =(f(x2)-f(x1))/(x2-x1)

hence

therefore rate of change of f(x) is positive for 3 <=x<=8

therefore rate of change of f(x) is negative for 0 <=x<=3

rate of chage is greatest at about x=8

x 0 1 2 3 4 5 6 7 8 f(|x) 18 12 8 6 7 8 15 18 30 f'(x) 0 -6 -4 -2 1 1 7 3 12

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