Without referring to Theorem 5.3.8, prove part (c) of Corollary 5.3.9. Ifis a finite collection of countable sets, then iscountable.
L26 - 9 Now You Try It (NYTI): 1. Find each interval on which f(x)i sicesngadderangfrechofhe following functions. Find all relative extrema. Find the intervals on which the function is concave up and down, and ﬁnd each inﬂection point. 9 (a) f(x)= x + x (b) f(x)= xln(x) (c) f(x)=3 x 1/3− x 2. Suppose the function f has second derivative ▯▯ 2 4 3 2 f (x)= x (x − 3) (x +2) (x − 1). (a) How many inﬂection points does f have Where do they occur (b) Suppose f has horizontal tangent lines at x = −5, 0, 1 and 2. Which