Question

iv) f(x)=1-3(x-1)^2/3 on [0, 2] verify rolles theorem
​

Answer 1

Answer:

From Fig. 11, we observe that tangents at P as well as Q are parallel to x-axis, therefore, f ′ (x) at P and also at Q are zero. Thus, there exists at least one value c of x in (a,b) such that f ′ (c) = 0. Hence, the Rolle's theorem is verified.