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question 123

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For the function For the function   : ​ (a) Find the critical numbers of f (if any) ; (b) Find the open intervals where the function is increasing or decreasing;and (c) Apply the First Derivative Test to identify all relative extrema. ​ Then use a graphing utility to confirm your results. ​ A) (a)    (b) increasing:   ;decreasing:   (c) relative max:   ;relative min:   ​ B) (a)    (b) decreasing:   ;increasing:   (c) relative min:   ;relative max:   ​ C) (a)    (b) increasing:   ;decreasing:   (c) relative max:   ;no relative min.​ D) (a)    (b) increasing:   ;decreasing:   ​(c) relative max:   ;relative min:   ​​ E) (a)    (b) decreasing:   ;increasing:   (c) relative min:   ;relative max:  : ​
(a) Find the critical numbers of f (if any) ;
(b) Find the open intervals where the function is increasing or decreasing;and
(c) Apply the First Derivative Test to identify all relative extrema.

Then use a graphing utility to confirm your results.

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Definitions:

Hindbrain

The rearmost segment of the brain, including structures such as the cerebellum and medulla oblongata, involved in regulating basic life functions.

Cerebellum

A region of the brain that plays an important role in motor control, and it may also be involved in some cognitive functions such as attention and language as well as in regulating fear and pleasure responses.

Interneurons

A type of neuron located within the central nervous system that acts as a link between sensory neurons and motor neurons, processing information.

Dendrites

Branch-like extensions of neurons that receive signals from other neurons and conduct them toward the cell body.

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