Limits and Differentiation Test

Result

Limits and Differentiation Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

The number of points at which the function f(x) = max. {a – x, a + x, b}, – ∞ < x < ∞, 0 < a < b cannot be differentiable is

A
1

B
2

C
3

D
none

Solution

The function will not be differentiable at a-x = b, and a+x = b or at (+_(b-a)). This is becasue the definition of the question would change at these points.

Easiest way to solve this is by drawing the graph.
Question 2
1 / -0

If f(x) is differentiable everywhere, then

A
|f| is differentiable everywhere

B
|f|² is differentiable everywhere

C
f |f| is not differentiable at some point

D
f + |f| is differentiable everywhere
Question 3
1 / -0

A function f defined as f(x) = x[x] for –1 ≤ x ≤ 3 where [x] defines the greatest integer ≤ x is

A
continuous at all points in the domain of f but non-derivable at a finite number of points

B
discontinuous at all points & hence non-derivable at all points in the domain of f

C
discontinuous at a finite number of points but not derivable at all points in the domain of f

D
discontinuous & also non-derivable at a finite number of points of f

Solution

f(x) = x [x]; –1 ≤ x ≤ 3.
Since, Greatest Integral function are not continuous as well as differentiable at Integers.
∴ Option D. is correct answer.