Mathematics · 2021
JEE Main · 4 August 2021, Shift 2 · Q87
If f be a twice differentiable function satisfying f(x)=x^4+x^2 f^′ ′(1)+f^′ ′(2), then the modulus of the minimum value of f(x) is equal to \ \ \ \.
If $\displaystyle f$ be a twice differentiable function satisfying $\displaystyle f(x)=x^4+x^2 f^{\prime \prime}(1)+f^{\prime \prime}(2)$, then the modulus of the minimum value of $\displaystyle f(x)$ is equal to \_\_\_\_.
Official answer
12
More from Methods of Differentiation
- Let f(x)=( sin ( tan^-1 x)+ sin ( cot^-1 x))^2-1, |x|>1. If (d y)/(d x)=1/2 d/(d x)( sin^-1(f(x))) and y(√3)=(π)/6, then y(-√3) is equal to:2020
- If y(x)=x^x, x>0, then y^′ ′(2)-2 y^′(2) is equal to:2023
- If 2 x^y+3 y^x=20, then (d y)/(d x) at (2,2) is equal to:2023
- If y(x)=(x^x)^x, x>0, then (d^2 x)/(d y^2)+20 at x=1 is equal to \ \ \ \.2022
- Suppose for a differentiable function h, h(0)=0, h(1)=1 and h^′(0)=h^′(1)=2. If g(x)=h(e^x) e^h(x), then g^′(0) is equal to:2024
- If y=Σ_k=1^6 k cos^-1{3/5 cos k x-4/5 sin k x}, then (d y)/(d x) at x=0 is \ \ \ \.2020
- Let f: S → S where S=(0, ∞) be a twice differentiable function such that f(x+1)=x f(x). If g: S → R be defined as g(x)= log_e f(x), then the value of…2021
- For the curve C:(x^2+y^2-3)+(x^2-y^2-1)^5=0, the value of 3 y^′-y^3 y^′ ′, at the point (α, α), α>0, on C, is equal to \ \ \ \.2022
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.