15) Give an example of a function defined on (a,b) that is not continuous on (a,b) but attains both relative and absolute extrema.
4) prove that between two consecutives roots f(x)=1–e^x sin x there exists at least one root of g(x) = 1 + e^x cos x.Glue a funct (a,6) that is on ex cmp la o defined on in d chains absolut c extrema 4) pr two there ex H at least one rout e (OS X
f(x) = 1 - x^x * sin(x)
x(x) = x xxxx xxx(x) = x^(-x)
xxx xx xx plot xxx(x) and x^(-x), xx xxx that xxx curves xxxxxxxxx xx xxxx positive xxxxx of xxx(x). x.x. xxx first xxxxxxxxxxxx is xx x < x < /2 xxx xxx xxxxxx at /x < x < . Consecutive xxxxxxxxxxxxx are xx
xxxxx x_i xxx x_x xxx consecutive xxxxx of x(x).
[xxxxxxx xx xxx quadrants xx x_i xxx x_x]
= 1 ± (x^(xx) - 1)
xxxxx x_j > /x, x^(x*x_x) > x, thus x(x_x) < x
xxxxx x_i xxx x_x xxx consecutive xxxxx of x(x) xxx