If f (x) = min \ 9 - x^ 2 , 1 + x^ 2 \ , x ∈ [-3,3], then the...

f \left(x\right) = min \left\{\sqrt{9 - x^{2}}, \sqrt{1 + x^{2}}\right\}, \forall x \in \left[-3,3\right], then

the number of point(s) wheref \left(x\right) is non-differentiable is/are $If f (x) = min \ 9 - x^ 2 , 1 + x^ 2 \ , x ∈ [-3,3], then the number of point(s) wheref (x) is non-differentiable is/are$

Options

A $4$
B $3$
C $2$
D $0$

Correct answer

A. $4$

Step-by-step solution

Using graph of

y = \sqrt{9 - x^{2}} ⇒ x^{2} + y^{2} = 9

y = \sqrt{1 + x^{2}} ⇒ y^{2} - x^{2} = 1

In the figure, we can see the graph of

f \left(x\right)

$If f (x) = min \ 9 - x^ 2 , 1 + x^ 2 \ , x ∈ [-3,3], then the number of point(s) wheref (x) is non-differentiable is/are$
Clearly,

f

\left(x\right)

is non-differentiable at<br />

x = - 3, {x}_{1}, {x}_{2}, 3

(4

points)
because there are sharp points at

{x}_{1}, {x}_{2}

and at

x = 3,x = – 3

there are vertical tangents.

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

Let ℝ denote the set of all real numbers. Let f : ℝ arrow ℝ be an arbitrary function and… JEE Advanced 2026 Consider the function f : (-(π)/(2), (π)/(2)) arrow (-∞, ∞) defined by f(x) = (|x| + |x… JEE Advanced 2026 For a real number α , let [α] denote the greatest integer less than or equal to α . For a… JEE Advanced 2026 For the function f(x) = e^ |x| - |x| , x ∈ ℝ , consider the following statements… JEE Main 2026 Let f(x) = cases (1)/(3), & x ≤ π/2 (b(1- x))/((π-2x)^2), & x > π/2 cases . If f is… JEE Main 2026 Let f(x) = cases x^3 + 8 ; & x Then the number of points, where the function g ∘ f is… JEE Main 2026 Let f(x)= cases e^ x-1 , & x<0 x^2-5x+6, & x ≥ 0 cases and g(x)=f(|x|)+|f(x)| . If the… JEE Main 2026 The number of points, at which the function f(x) = \ 6x, 2 + 3x^2\ + |x - 1|| |x^2… JEE Main 2026 The number of points in the interval [2, 4] , at which the function f(x) = [x^2 - x… JEE Main 2026 Let f(x)= _ θ arrow 0 ( π x-x^ ((2)/(θ)) (x-1) 1+x^ ((2)/(θ)) (x-1) ), x ∈ R . Consider… JEE Main 2026 Let [t] denote the greatest integer less than or equal to t . If the function f(x)=\… JEE Main 2026 If the function f(x)= e^ x (e^ x-x -1)+ _ e ( x+ x)-x x-x is continuous at x=0 , then the… JEE Main 2026 Let α, β ∈ ℝ be such that the function f(x)= cases 2 α(x^ 2 -2)+2 β x &, x be… JEE Main 2026 If f(x)=\ array cc a|x|+x^ 2 -2( |x|)( |x|) x &, x ≠ 0 b &, x=0 array . is continuous at… JEE Main 2026 Let f(x)= cases a x^ 2 +2 a x+3 4 x^ 2 +4 x-3 &, x ≠-(3)/(2), (1)/(2) ~b &, x=-(3)/(2)… JEE Main 2026 Let [·] denote the greatest integer function, and let f(x)= \ 2 x, x^ 2 \ . Let S = \ x… JEE Main 2026 Full Continuity and Differentiability list Continuity and Differentiability JEE Maths PYQs JEE Mathematics PYQs All NTA Abhyas JEE Main PYQs