Question:
Let f(x)=max{5x, 52-2x2 }, where x is any positive real number. Then the minimum possible value of f(x) is
Let f(x)=max{5x, 52-2x2 }, where x is any positive real number. Then the minimum possible value of f(x) is
Updated On: Sep 30, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 20
Solution and Explanation
Given x is positive real number. The minimum value of the maximum {5x,52-2x2} will occur when both the graphs intersect. i.e., when 5x = 52-2x2
2x2+5x-52 = 0
2x2+13x-8x-52 = 0
x(2x+13)-4(2x+13) = 0
(x-4)(2x+13) = 0
x = 4 or -13/2
When x = 4, f(x) = 20
Was this answer helpful?
0
0
Top Questions on Functions
- If $ f(x) = 2x^2 - 3x + 5 $, find $ f(3) $.
- Determine those values of $x$ for which $f(x) = \frac{2}{x} - 5$, $x \ne 0$ is increasing or decreasing.
Let A be the set of 30 students of class XII in a school. Let f : A -> N, N is a set of natural numbers such that function f(x) = Roll Number of student x.
Give reasons to support your answer to (i).- Assertion (A): Let \( A = \{ x \in \mathbb{R} : -1 \leq x \leq 1 \} \). If \( f : A \to A \) be defined as \( f(x) = x^2 \), then \( f \) is not an onto function.
Reason (R): If \( y = -1 \in A \), then \( x = \pm \sqrt{-1} \notin A \). Find the domain of the function \( f(x) = \cos^{-1}(x^2 - 4) \).
View More Questions
Questions Asked in CAT exam
- When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become
- CAT - 2024
- Ratio and Proportion
- Two points A and B are 45 km apart. Anil started from A. Sunil started from B. They met each other after 1 hour 30 mins. and after meeting, they continued towards their destinations. Time taken by Anil to reach Point B was 1 hr 15 mins more than the time taken by Sunil to reach point A. Find speed of Anil
- CAT - 2024
- Time, Speed and Distance
- The sum of all four-digit numbers that can be formed with the distinct non-zero digits $a$, $b$, $c$, and $d$, with each digit appearing exactly once in every number, is $153310 + n$, where $n$ is a single digit natural number. Then, the value of $(a + b + c + d)$ is ?
- CAT - 2024
- Permutations and Combinations
- The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
- CAT - 2024
- Profit and Loss
- In the $XY$-plane, the area, in sq. units, of the region defined by the inequalities $y \ge x + 4$ and $-4 \le x^2 + y^2 + 4(x - y) \le 0$ is
- CAT - 2024
- Coordinate Geometry
View More Questions