(a)(i) Identify the critical numbers of f. (Enter your answers as a comma-separa

Question

(a)(i) Identify the critical numbers of f. (Enter your answers as a comma-separated list.)
x =


(ii) Identify the open interval(s) on which f is increasing or decreasing. (Enter your answer using interval notation.)

increasing    


decreasing    

(iii) Determine whether f has a relative maximum, a relative minimum, or neither at each critical number. (Enter your answers as a comma-separated list.)

[WebAssign Plot]
i) Identify the critical numbers of f. (Enter your answers as a comma-separated list.)
x =


(ii) Identify the open interval(s) on which f is increasing or decreasing. (Enter your answer using interval notation.)

increasing    


decreasing    

(iii) Determine whether f has a relative maximum, a relative minimum, or neither at each critical number. (Enter your answers as a comma-separated list.)

x =

(ii) Identify the open interval(s) on which f is increasing or decreasing. (Enter your answer using interval notation.)

(iii) Determine whether f has a relative maximum, a relative minimum, or neither at each critical number. (Enter your answers as a comma-separated list.)

(i) Identify the critical numbers of f. (Enter your answers as a comma-separated list.)
x =


(ii) Identify the open interval(s) on which f is increasing or decreasing. (Enter your answer using interval notation.)

increasing    


decreasing    

relative minimum     x =


relative maximum     x =

Explanation / Answer

at critical point , f ' =0 or f ' is undefined

when f increases, f '>0

when f decreases, f '<0

at relative minimum , f ' changes from negative to positive

at relative maximum , f ' changes from positive to negative

---------------------------------------------------------------

1)

critical number is x=0

increasing in (3,)

decreasing in (-,3)

relative minimum ,x =3

relative maximum ,x =DNE

---------------------------------------------------------------

2)

critical numbers are x=0,1

increasing in (-,0),(1,)

decreasing in (0,1)

relative minimum ,x =1

relative maximum ,x =0

---------------------------------------------------------------

3)

critical numbers are x=0,1,2

increasing in (-,0),(1,2)

decreasing in (0,1),(2,)

relative minimum ,x =1

relative maximum ,x =0,2

--------------------------------------------

4)

critical numbers are x=-3,1,5

increasing in (-3,1),(1,5)

decreasing in (-,-3),(5,)

relative minimum ,x =-3

relative maximum ,x =5

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