﻿ Let f : R → R be a function defined by f (x) =  max. {x; x3}. The set of all points where f (x) is not differentiable is: : Kaysons Education

# Let f : R → R be A Function Defined By f (x) =  max. {x; x3}. The Set Of All Points Where f (x) Is Not Differentiable Is:

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## Question

### Solution

Correct option is

{–1, 0, 1}

f (x) = max. {xx3}. Consider the graph separately of y = x3 and y = xand find their point of intersection;

i.e.,    x3 = x

⇒      x = 0, 1, –1

Now, to find f (x) = max. {xx3

Neglecting the graph below the point of intersection we get the required graph of f (x) = max. {xx3}.

Thus, from above graph,

Which shows f (x) is not differentiable at 3 points i.e., x = {–1, 0, 1}. (due to sharp edges)

#### SIMILAR QUESTIONS

Q1

Fill in the blank, statement given below let . The set of points where f (x) is twice differentiable is ……………. .

Q2

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Q3
Q4

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Q5

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Q6

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Q7

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Q8

Let f be a real function satisfying f (x + z) = f (xf (yf (zfor all real xyz . If f (2) = 4 and f’ (0) = 3. Then find f (0) and f’ (2).

Q9

Let h(x) = min.{xx2} for every real number of x. Then:

Q10

Let f (x) = Ï•(x) + ψ(x) and Ï•(a), ψ’(a) are finite and definite. Then: