h' = 5a(-2x+1)^4 (-2) = -10a(-2x+1)^4
h'' = 80a(-2x+1)^3
Since h' >=0 for all x, it is monotonic
h'=0 ==> (-2x+1)^4 = 0, independent of a,b
Consider the function h(x) = a(-2x+1)^5-b, where a doesn't equal 0 and b doesn't equal 0 are constants.
A. Find h'(x) and h"(x)
B. show that h is monotonic ( that is, that either h always increases or remains constant or h always decreases or remains constant)
C. Show that x-coordinate(s) of the location(s) of the critical points are independent of a and b.
1 answer
1 answer