Use the inequalities in Exercise 70 to estimate (0.1) if (x) = 1/(1 + x 4 cos

Use the inequalities in Exercise 70 to estimate ƒ(0.1) if ƒ′(x) = 1/(1 + x⁴ cos x) for 0 ≤ x ≤ 0.1 and ƒ(0) = 1.

Exercise 70

Let ƒ be a function defined on an interval [a, b]. What conditions could you place on ƒ to guarantee that

where min ƒ′ and max ƒ′ refer to the minimum and maximum values of ƒ′ on [a, b]? Give reasons for your answers.

Transcribed Image Text:

min f' ≤ f(b) f(a) b - a < max f',