Monotonicity

JEE Main Mathematics · Applications of Derivatives · 14 questions, latest first

• Consider the following three statements for the function f:(0, ∞) → R defined by f(x)=| log_e x|-|x-1|: (I) f is differentiable…202624 January, Shift 2 · Q17
• Let f: R → R be a twice differentiable function such that f^′ ′(x)>0 for all x ∈ R and f^′(a-1)=0, where a is a real number. Let…202621 January, Shift 2 · Q18
• Let f: R → R be a twice differentiable function such that the quadratic equation f(x) m^2-2 f^′(x) m+f^′ ′(x)=0 in m, has two…202621 January, Shift 1 · Q24
• Let the function f(x)=x/3+3/x+3, x ≠ 0 be strictly increasing in (-∞, α_1) ∪(α_2, ∞) and strictly decreasing in (α_3, α_4) ∪(α_4,…20258 April, Shift 2 · Q17
• Let (2,3) be the largest open interval in which the function f(x)=2 log_e(x-2)-x^2+a x+1 is strictly increasing and (b, c) be the…202524 January, Shift 2 · Q18
• For the function f(x)=( cos x)-x+1, x ∈ R, between the following two statements (S1) f(x)=0 for only one value of x in [0, π].…20248 April, Shift 1 · Q7
• The interval in which the function f(x)=x^x, x>0, is strictly increasing is20246 April, Shift 1 · Q9
• For the function f(x)= sin x+3 x-2/(π)(x^2+x), where x ∈[0, (π)/2], consider the following two statements: (I) f is increasing in…20245 April, Shift 1 · Q5
• If 5 f(x)+4 f(1/x)=x^2-2, ∀ x ≠ 0 and y=9 x^2 f(x), then y is strictly increasing in:20241 February, Shift 1 · Q7
• The function f(x)=x/(x^2-6 x-16), x ∈ R-{-2,8}202429 January, Shift 2 · Q7
• Let g(x)=3 f(x/3)+f(3-x) and f^′ ′(x)>0 for all x ∈(0,3). If g is decreasing in (0, α) and increasing in ( α, 3 ), then 8 α is:202427 January, Shift 2 · Q10
• Let g(x)=f(x)+f(1-x) and f^′ ′(x)>0, x ∈(0,1). If g is decreasing in the interval (0, α) and increasing in the interval (α, 1),…202310 April, Shift 2 · Q9
• Let f(x)=2 x+ tan^-1 x and g(x)= log_e(√(1+x^2)+x), x ∈[0,3]. Then20231 February, Shift 1 · Q69
• Let f:(0,1) → R be a function defined by f(x)=1/(1-e^-x), and g(x)=(f(-x)-f(x)). Consider two statements (I) g is an increasing…202325 January, Shift 1 · Q73