Solução_Calculo_Stewart_6e

F.
TX.10 SECTION 4.3 HOW DERIVATIVES AFFECT THE SHAPE OF A GRAPH ¤ 165
f(b) = 1 4
1+
√
3
,andf(c) =1. To show that these three points of inflection lie on one straight line, we’ll show that the
slopes m ac and m bc are equal.
m ac =
m bc =
f(c) − f(a)
c − a
f(c) − f(b)
c − b
= 1 − √
1
4 1 − 3
3
1 − −2 − √ 3 = + √ 1
4 4 3
3+ √ 3 = 1 4
= 1 − √
1
4 1+ 3
3
1 − −2+ √ 3 = − √ 1
4 4 3
3 − √ 3 = 1 4
71. Suppose that f is differentiable on an interval I and f 0 (x) > 0 for all x in I except x = c. Toshowthatf is increasing on I,
let x 1, x 2 be two numbers in I with x 1