By Ib Elite Tutor at 0:01 am, May 12, 2017
Differentiability Evaluate functions:
1.
1 x x 1 f(x) = (1 x )(2 x ) 1 x 2 3 x x2
Discuss continuity and differentiability of above function. 2.
x 2 3x a f(x) = bx z
for x 1 for x 1
If above function is differentiable every where find a and b. 3.
Discuss the differentiability of f ( x ) log e x , for x > 0.
4.
Discuss differentiability of f(x) = |x – 1| + |x – 2|.
5.
e1/ x e 1/ x x If f ( x) e1/ x e 1/ x 0
, x 0 x0
Then show that f(x) is not differentiable at x = 0.
6.
x 1 ax x 1 b, f ( x) x 1 1 x 3 px 2 qx 2 x3
If f(x) is continuous at x ≤ R and f(x) is not differentiable at x = 1 then find a, b, p and q. 7.
1 2 ( x 1) sin x f ( x) x 1 1
x 1 x 1
Find all points where f(x) is differentiable. 8. 9.
Show that f(x) = |x| is not differentiable at x = 0.
1 2 x sin if x 0 f ( x) x 0 if x 0 Show that f(x) is differentiable at x = 0 and f′ (0) = 0.