Global Maxima and Minima

JEE Main Mathematics · Applications of Derivatives · 12 questions, latest first

• Let f: R → R be a differentiable function such that f((x+y)/3)=(f(x)+f(y))/3 for all x, y ∈ R, and f^′(0)=3. Then the minimum…20265 April, Shift 1 · Q19
• max_0 ≤ x ≤ π(16 sin (x/2) cos^3(x/2)) is equal to:20264 April, Shift 2 · Q12
• Let f(x)=x^2025-x^2000, x ∈[0,1] and the minimum value of the function f(x) in the interval [0,1] be (80)^80(n)^-81. Then n is…202622 January, Shift 1 · Q16
• Let x=-1 and x=2 be the critical points of the function f(x)=x^3+a x^2+b log_e|x|+1, x ≠ 0. Let m and M respectively be the…20257 April, Shift 1 · Q17
• Let f(x)=∫_0^x t(t^2-9 t+20) dt, 1 ≤ x ≤ 5. If the range of f is [α, β], then 4(α+β) equals:202529 January, Shift 2 · Q18
• Let f(x)=3 √(x-2)+√(4-x) be a real valued function. If α and β are respectively the minimum and the maximum values of f, then…20244 April, Shift 2 · Q7
• Let the sum of the maximum and the minimum values of the function f(x)=(2 x^2-3 x+8)/(2 x^2+3 x+8) be m/n, where gcd(m, n)=1.…20244 April, Shift 1 · Q12
• Let f(x)=(x+3)^2(x-2)^3, x ∈[-4,4]. If M and m are the maximum and minimum values of f, respectively in [-4, 4], then the value…202430 January, Shift 2 · Q9
• max_0 ≤ x ≤ π{x-2 sin x cos x+1/3 sin 3 x}=202313 April, Shift 1 · Q10
• If a_α is the greatest term in the sequence a_n=n^3/(n^4+147), n=1,2,3, …, then α is equal to ____.20238 April, Shift 1 · Q23
• The sum of the absolute maximum and minimum values of the function f(x)=|x^2-5 x+6|-3 x+2 in the interval [-1,3] is equal to:20231 February, Shift 2 · Q69
• The absolute minimum value, of the function f(x)=|x^2-x+1|+[x^2-x+1], where [t] denotes the greatest integer function, in the…202331 January, Shift 2 · Q68