Diff. (x2 – 5x + 8) (x3 + 7x + 9) by
(i) product rule
(ii) expanding the product to obtain a single polynomial.
(iii) logarithmic differentiation.
Do they give the same answer ?
Examine if Rolle’s theorem is applicable to any of the following functions. Can you say something about the converse of Rolle’s theorem from these examples ?
(i) f(x) = [x] on [5, 9]
(ii) f(x) = [x] on [–2, 2]
(iii) f(x) = x2 – 1 on [1, 2]
Find the absolute
maximum value and minimum value of the following functions in the given
intervals:
I.f(x)
= x3,
II.f(x) = sin
x + cos x,
III.f(x) = 4x
IV.f(x) = (x ? 1)2
+ 3x