Use the inequalities in Exercise 70 to estimate (0.1) if (x) = 1/(1 - x 4 ) for 0 x 0.1 and (0)

Use the inequalities in Exercise 70 to estimate ƒ(0.1) if ƒ′(x) = 1/(1 - x⁴) for 0 ≤ x ≤ 0.1 and ƒ(0) = 2.

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.

min f' f(b) f(a) b - a < max f',