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Clear step by step for these 2 problems? (max & min)(concavity)

Posted 9 years ago

Hello, could anyone give clear step by steps to solve these problems? Thank you.

1) Let f(x)=4x?8x for x greater than 0. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

  1. f is increasing on the intervals :______________
  2. f is decreasing on the intervals:_____________
  3. The relative maxima of f occur at x =_____________
  4. The relative minima of f occur at x =______________

Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none". In the last two, your answer should be a comma separated list of x values or the word "none".


2)Let f(x)=1/(5x^(2)+7). Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f.

  1. f is concave up on the intervals:____________
  2. f is concave down on the intervals:____________
  3. The inflection points occur at x =____________

Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none". In the last one, your answer should be a comma separated list of x values or the word "none".

POSTED BY: K M

Look at the first derivative to see where the function is increasing or decreasing and look at the second derivative to see where the function is concave up or concave down.

POSTED BY: Frank Kampas
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