Mathematics · 2021
JEE Main · 24 February 2021, Shift 1 · Q67
The function f(x)=(4 x^3-3 x^2)/6-2 sin x+(2 x-1) cos x:
The function $\displaystyle f(x)=\frac{4 x^3-3 x^2}{6}-2 \sin x+(2 x-1) \cos x$ :
Official answer
(1)
increases in $\displaystyle \left[\frac{1}{2}, \infty\right)$
More from Applications of Derivatives
- 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, α_5). Then Σ_i=1^5…2025
- 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 function in (0,1)…2023
- A wire of length 20 m is to be cut into two pieces. A piece of length l_1 is bent to make a square of area A_1 and the other piece of length l_2 is…2023
- Let f: R → R be a function defined by f(x)=(x-3)^n_1(x-5)^n_2, n_1, n_2 ∈ N. Then, which of the following is NOT true?2022
- Let f(x)=x cos^-1(- sin |x|), x ∈[-(π)/2, (π)/2], then which of the following is true?2020
- Let f(x)=2 x+ tan^-1 x and g(x)= log_e(√(1+x^2)+x), x ∈[0,3]. Then2023
- If the tangent to the curve y=x+ sin y at a point (a, b) is parallel to the line joining (0, 3/2) and (1/2, 2), then:2020
- 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, respectively, such that…2025
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.