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).
- f is increasing on the intervals :______________
- f is decreasing on the intervals:_____________
- The relative maxima of f occur at x =_____________
- 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.
- f is concave up on the intervals:____________
- f is concave down on the intervals:____________
- 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".