Let f- R - R be a function defined by fx-maxx- x 3- then-A- fx is discontinuous at 3 pointsB- fx is not differentiable at 3 pointsC- fx is continuous at all pointsD- fx is not differentiable at x-0

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Differentiability

Let f: R → R ...

Question

Let f: R $\to$ R be a function defined by f(x) = max {x, $x^{3}$ }, then-

f (x) is discontinuous at 3 points

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f (x) is not differentiable at 3 points

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f(x) is continuous at all points

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f (x) is not differentiable at x = 0

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Solution

The correct options are
B
f (x) is not differentiable at 3 points

C
f(x) is continuous at all points

D
f (x) is not differentiable at x = 0

y= $x^{3}$
Clearly not differentiable at x= 0, ±1.

$2^{n d}$ method

Solving $x^{3}$ = x, we have x= 0, ±1

$∴$ Max {x, $x^{2}$ }= x when x $<$ -1

= $x^{3}$ when -1 $\leq$ x $\leq$ 0

= x when 0 $<$ x $\leq$ 1

= $x^{3}$ when x $<$ 1

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Let f: R → R be a function defined by f(x) = max {x, x3}, then-

Let f: R $\to$ R be a function defined by f(x) = max {x, $x^{3}$ }, then-