Limits, Continuity and Differentiability Test

Result

Limits, Continuity and Differentiability Test - 36

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Weekly Quiz Competition

Question 1
4 / -1

Let f be differentiable for all x. If f(1) = –2 and f \' (x) ≥ 2 for x ϵ [1,6], then

A
f(6) < 5

B
f(6) = 5

C
f(6) ≥ 8

D
f(6) < 8

Solution
Question 2
4 / -1

f(x) = ||x| – 1| is not differentiable at

A
0

B
±1, 0

C
1

D
±1

Solution
Question 3
4 / -1

Let f be continuous on [1,5] and differentiable in (1,5).If f(1) = –3 and f\'(x) ≥ 9 for all x ∈(1,5) , then

A
f(5) ≥ 33

B
f(5) ≤ 36

C
f(5) ≥ 9

D
f(5) ≤ 9

Solution
Question 4
4 / -1

A
0

B
1

C
2

D
3

Solution
Question 5
4 / -1

Let f(x + y) = f(x) + f(y) and f(x) = x²g(x) for all x,y ∈ R, where g(x) is continuous function. Then f \' (x) is equal to

A
g' (x)

B
g(0)

C
g(0) + g'(x)

D
0

Solution
Question 6
4 / -1

The function f(x) = (x² – 1) |x² – 3x + 2| + cos (|x|) is not differentiable at

A
–1

B
0

C
1

D
2

Solution
Question 7
4 / -1

A
|x| < 1

B
x = 1, –1

C
|x| > 1

D
None of these

Solution
Question 8
4 / -1

The number of points at which the function f(x) = |x – 0.5| + |x – 1| + tan x does not have a derivative in the interval (0,2), is

A
1

B
2

C
3

D
4

Solution
Question 9
4 / -1

If f(x) is a function such that f\" (x) + f(x) = 0 and g(x) = [f(x)]² + [f\' (x)]² and g(3) = 3, then g(8) =

A
5

B
0

C
3

D
8

Solution
Question 10
4 / -1

A
0

B
1

C
2

D
–2

Solution