Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2014Paper 1
Exam
JEE Advanced
Year
2014
Paper
Paper 1
Subject
Mathematics
Chapter
Application of Derivatives

JEE Advanced 2014 · Paper 1 · Mathematics · Application of Derivatives

Let a ∈ R and let f: R → R be given by f(x) = x ^ 5 - 5x + a, then

Let a∈Ra \in R and let f:R→Rf: R \to R be given by f(x)=x5−5x+a,f\left(x\right) = {x}^{5} - 5x + a, thenLet a ∈ R and let f: R → R be given by f(x) = x ^ 5 - 5x + a, then

Options

  1. Aff\left(x\right)hasthreerealrootsifhas three real roots ifa > 4
  2. Bff\left(x\right)hasonlyonerealrootsifhas only one real roots ifa > 4
  3. Cff\left(x\right)hasthreerealrootsifhas three real roots ifa < - 4
  4. Dff\left(x\right)hasthreerealrootsifhas three real roots if- 4 < a < 4

Correct answer

B. ff\left(x\right)hasonlyonerealrootsifhas only one real roots ifa > 4

Step-by-step solution

Let y=x5−5xy = {x}^{5} - 5x

Let a ∈ R and let f: R → R be given by f(x) = x ^ 5 - 5x + a, then

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Consider the function f: (0, ∞) arrow (-∞, ∞) given by f(x) = x \, _e(x) - x + 1 . Then… JEE Advanced 2026Let P be the point on the parabola y = x^2 such that the slope of the tangent to the… JEE Advanced 2026Let f: ℝ arrow ℝ be a differentiable function such that f((x+y)/(3)) = (f(x) + f(y))/(3)… JEE Main 2026_ 0 ≤ x ≤ π (16 ((x)/(2)) ^3((x)/(2))) is equal to: JEE Main 2026Let f(x) be a polynomial of degree 5 , and have extrema at x = 1 and x = -1 . If _ x → 0… JEE Main 2026The number of critical points of the function f(x) = cases |( x)/(x)|, & x ≠ 0 1, & x = 0… JEE Main 2026Let f be a differentiable function satisfying f(x)=1-2 x+∫_ 0 ^ x e^ (x-t) f(t) dt, x ∈ R… JEE Main 2026Consider the following three statements for the function f:(0, ∞) arrow ℝ defined by… JEE Main 2026Let (2 α, α) be the largest interval in which the function f(t)= |t+1| t^ 2 , t 2 , is… JEE Main 2026Let f(x)=x^ 2025 -x^ 2000 , x ∈[0,1] and the minimum value of the function f(x) in the… JEE Main 2026Let f: ℝ → ℝ be a twice differentiable function such that f''(x) > 0 for all x ∈ ℝ and… JEE Main 2026Let f: R arrow R be a twice differentiable function such that the quadratic equation f(x)… JEE Main 2026Let ℝ denote the set of all real numbers. Define the function f: R arrow R by f(x)=\… JEE Advanced 2025Let ℝ denote the set of all real numbers. For a real number x , let [x] denote the… JEE Advanced 2025Let ℝ denote the set of all real numbers. Let f: ℝ arrow ℝ be defined by f(x)= cases (6… JEE Advanced 2025Let the function f(x)=(x)/(3)+(3)/(x)+3, x ≠ 0 be strictly increasing in (-∞, α_1) U(α_2… JEE Main 2025 Full Application of Derivatives list Application of Derivatives JEE Maths PYQsJEE Mathematics PYQs All JEE Advanced PYQs