Homework SourseOn what intervals is the function fxx88x7 both decreasing an
On what intervals is the function f(x)=x^8-8x^7 both decreasing and concave up?
interval(s) =
Please explain
(Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10) .)
interval(s) =
Please explain
(Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10) .)
Solution
f(x) =x^7(x-8)
dfx/dx =8x^7-56x^6
ie 8x^6(x-7)
at x =0 dfx/dx =0
t x=7 dfx/dx =0
from 0 to 7 dfx/dx<0
and from greater than 7 dfx/dx >0... hence concave up
and from -ve infinty to zero dfx/dx <0
hence in interval (0,7) f(x) is both decreasing and concave up
