Let n \geq 2 be a natural number and f:[0,1] \to \mathbb{R} be the function defined by f(x)={\\begin{array}{cc}n(1-2 n x) & \\\\text{ if }\\ 0 \leq x \leq \\\{1\end\frac{array}{2 n} ; 2 n(2 n x-1) , \text{ if } \frac{1}{2 n} \leq x \leq \frac{3}{4 n} ; 4 n(1-n x) , \text{ if } \frac{3}{4 n} \leq x \leq \frac{1}{n} ; \frac{n}{n-1}(n x-1) , \text{ if } \frac{1}{n} \leq x \leq 1 }. If n is such that the area of the region bounded by the curves x=0, x=1, y=0 and y=f(x) is 4 , then the maximum value of the function f is [JEE Adv 2023 P1]

Application of Integration

Section: Mathematics

Question : 4 of 28

Marks: +1, -0

Let n≥2 be a natural number and f:[0,1]→ℝ be the function defined by
f(x)={

n(1−2nx)

‌ if ‌0≤x≤‌

2n(2nx−1)

‌ if ‌‌

≤x≤‌

4n(1−nx)

‌ if ‌‌

≤x≤‌

‌

n−1

(nx−1)

‌ if ‌‌

≤x≤1

.
If n is such that the area of the region bounded by the curves x=0,x=1,y=0 and y=f(x) is 4 , then the maximum value of the function f is

[JEE Adv 2023 P1]

Go to Question:

Prev Question

Next Question