Let a, b ∈ R and f: R arrow R be defined by f(x)=a cos ( mid x3-x]+b|x| sin (|x3+x|). Then f is

Question

Let a, b ∈ R and f: R arrow R be defined by f(x)=a cos ( mid x3-x]+b|x| sin (|x3+x|). Then f is (A) differentiable at x=0 if a =0 and b =1 (B) differentiable at x=1 if a =1 and b =0 (C) NOT differentiable at x =0 if a =1 and b =0 (D) NOT differentiable at x =1 if a =1 and b =1

Tardigrade Admin · Accepted Answer

f: R arrow R f ( x )= a cos ( x 3- x )+ b | x | sin ( mid x 3+ x ) (A) at a=0 b=1 f(x) =0+|x| sin (|x3+x|) = begincasesx sin (x3+x) x<0 x sin (x3+x) x ≥ 0 endcases So f(x) differentiable at x=0 (B) at a =1 b =0 f ( x )= cos ( x 3- x ) is differentiable at x =1 (C) at a =1 b =0 f(x)= cos (x3-x) is differentiable at x=0 (D) at a=1 b=1 f ( x )= cos ( x 3- x )+ x sin ( x 3+ x ) is always differentiable

Q. Let $a, b \in R$ and $f : R \to R$ be defined by $f (x) = a cos (∣ x^{3} - x] + b ∣ x ∣ sin (∣ ∣ x^{3} + x ∣ ∣)$ . Then $f$ is

differentiable at $x = 0$ if $a = 0$ and $b = 1$

differentiable at $x = 1$ if $a = 1$ and $b = 0$

NOT differentiable at $x = 0$ if $a = 1$ and $b = 0$

NOT differentiable at $x = 1$ if $a = 1$ and $b = 1$

Q. Let a,b∈R and f:R→R be defined by f(x)=acos(∣x3−x]+b∣x∣sin(∣∣​x3+x∣∣​). Then f is

differentiable at x=0 if a=0 and b=1

differentiable at x=1 if a=1 and b=0

NOT differentiable at x=0 if a=1 and b=0

NOT differentiable at x=1 if a=1 and b=1

Q. Let $a, b \in R$ and $f : R \to R$ be defined by $f (x) = a cos (∣ x^{3} - x] + b ∣ x ∣ sin (∣ ∣ x^{3} + x ∣ ∣)$ . Then $f$ is

differentiable at $x = 0$ if $a = 0$ and $b = 1$

differentiable at $x = 1$ if $a = 1$ and $b = 0$

NOT differentiable at $x = 0$ if $a = 1$ and $b = 0$

NOT differentiable at $x = 1$ if $a = 1$ and $b = 1$