Set 8: Problem 18 Prev Up Next (1 pt) Suppose that f(x)-22 +2. (A) Find all crit

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Set 8: Problem 18 Prev Up Next (1 pt) Suppose that f(x)-22 +2. (A) Find all critical values of f. If there are no critical values, enter-1000. If there are more than one, enter them separated by commas Critical value(s) 0,4/3 (B) Use interval notation to indicate where f () is decreasing. Decreasing: (-inf,0) (C) Find the r-coordinates o all local maxima of f. If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas. Local maxima at 1 = (D) Find the r-coordinates of all local minima of f. If there are no locall minima, enter-1000. If there are more thar one, enter them separated by commas Local minima atr- Note: You can eam partial credit on this problem Preview Answers Submit Answers You have attempted this problem 3 times. Your overall recorded score is 25% PrtScn Home End PgUp PgDn InsD F6 F7 F12

Explanation / Answer

f(x) = x3-2x2+2

f '(x) = 3x2-4x

Critical number, f '(x) =0

3x2-4x=0

x(3x-4)=0

A . x =0 , 3/4

     In (-infinity,0), f '(x)>0

     In (0,3/4) , f '(x) <0

     In (3/4, infinity), f '(x) >0

     Increasing interval (-infinity,0)U(3/4, infinity)

B.    Decreasing interval (0,3/4)

     f ''(x) =6x-4

     at x=0 , f ''(x) = -4<0

     at x=3/4, f ''(x) =0.5>0

C.     local maximum is at x=0 and

D .     local minimum is at x=3/4

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