Local Maxima and Minima

JEE Main Mathematics · Applications of Derivatives · 16 questions, latest first

• Let f(x) be a polynomial of degree 5, and have extrema at x=1 and x=-1. If lim_x → 0((f(x))/x^3)=-5, then f(2)-f(-2) is equal to:20262 April, Shift 2 · Q18
• Let (2 α, α) be the largest interval in which the function f(t)=(|t+1|)/t^2, t<0, is strictly decreasing. Then the local maximum…202624 January, Shift 1 · Q24
• Let f: R → R be a polynomial function of degree four having extreme values at x=4 and x=5. If lim_x → 0 (f(x))/x^2=5, then f(2)…20257 April, Shift 2 · Q18
• Let a>0. If the function f(x)=6 x^3-45 a x^2+108 a^2 x+1 attains its local maximum and minimum values at the points x_1 and x_2…20254 April, Shift 2 · Q17
• Let f: R → R be a function defined by f(x)=||x+2|-2| x| |. If m is the number of points of local minima and n is the number of…20253 April, Shift 2 · Q16
• If the function f(x)=2 x^3-9 a x^2+12 a^2 x+1, where a>0, attains its local maximum and local minimum values at p and q,…20252 April, Shift 1 · Q8
• The sum of all local minimum values of the function f(x)= {1-2 x, x<-1; 1/3(7+2|x|), -1 ≤ x ≤ 2; 11/18(x-4)(x-5), x>2} is202528 January, Shift 1 · Q16
• Let f(x)=∫_0^x^2 (t^2-8 t+15)/(e^t) dt, x ∈ R. Then the numbers of local maximum and local minimum points of f, respectively, are:202522 January, Shift 2 · Q17
• Let the set of all positive values of λ, for which the point of local minimum of the function (1+x(λ^2-x^2)) satisfies…20249 April, Shift 1 · Q27
• If the function f(x)=2 x^3-9 a x^2+12 a^2 x+1, a>0 has a local maximum at x=α and a local minimum at x=α^2, then α and α^2 are…20248 April, Shift 2 · Q10
• Let f(x)=4 cos^3 x+3 √3 cos^2 x-10. The number of points of local maxima of f in interval (0,2 π) is20248 April, Shift 1 · Q9
• The function f(x)=2 x+3(x)^(2/3), x ∈ R, has202429 January, Shift 2 · Q8
• If the local maximum value of the function f(x)=((√(3 e))/(2 sin x))^sin^2 x, x ∈(0, (π)/2), is k/e, then (k/e)^8+k^8/e^5+k^8 is…202312 April, Shift 1 · Q9
• If the functions f(x)=x^3/3+2 b x+(a x^2)/2 and g(x)=x^3/3+a x+b x^2, a ≠ 2 b have a common extreme point, then a+2 b+7 is equal…202330 January, Shift 2 · Q69
• Let the function f(x)=2 x^3+(2 p-7) x^2+3(2 p-9) x-6 have a maxima for some value of x<0 and a minima for some value of x>0.…202325 January, Shift 2 · Q70
• Let x=2 be a local minima of the function f(x)=2 x^4-18 x^2+8 x+12, x ∈(-4,4). If M is local maximum value of the function f in…202325 January, Shift 1 · Q67