Differentiability at a Point

JEE Main Mathematics · Continuity and Differentiability · 8 questions, latest first

• For the function f(x)=e^sin |x|-|x|, x ∈ R, consider the following statements: Statement I: f is differentiable for all x ∈ R.…20268 April, Shift 2 · Q13
• Let α, β ∈ R be such that the function f(x)= {2 α(x^2-2)+2 β x, x<1; (α+3) x+(α-β), x ≥ 1} be differentiable at all x ∈ R. Then…202624 January, Shift 1 · Q18
• If f(x)= {x^3 sin (1/x), x ≠ 0; 0, x=0}, then20246 April, Shift 1 · Q8
• Let a and b be real constants such that the function f defined by f(x)= {x^2+3 x+a, x ≤ 1; b x+2, x>1} be differentiable on R.…202430 January, Shift 2 · Q8
• If the function f(x)= {1/(|x|), |x| ≥ 2; a x^2+2 b, |x|<2} is differentiable on R, then 48(a+b) is equal to ____.202430 January, Shift 1 · Q30
• Consider the function f:(0,2) → R defined by f(x)=x/2+2/x and the function g(x) defined by g(x)= {min {f(t)}, 0<t ≤ x and 0<x ≤…202427 January, Shift 2 · Q9
• Let k and m be positive real numbers such that the function f(x)= {3 x^2+k √(x+1), 0<x<1; m x^2+k^2, x ≥ 1} is differentiable for…20238 April, Shift 2 · Q25
• Let f(x)= {x^2 sin (1/x), x ≠ 0; 0, x=0} Then at x=0202324 January, Shift 1 · Q73