Join WhatsApp Icon CAT WhatsApp Group
Question 68

Let f(x)= $$\max(5x, 52-2x^2)$$, where x is any positive real number. Then the minimum possible value of f(x) 


Correct Answer: 20

Solution

Share

The minimum value of the function will occur when the expressions inside the function are equal.
So, 5$$x$$ = $$52 - 2x^2$$
or, $$2x^2 + 5x - 52$$ = 0
On solving, we get $$x$$ = 4 or $$-\dfrac{13}{2}$$
But, it is given that $$x$$ is a positive number.
So, $$x$$ = 4
And the minimum value = 5*4 = 20
Hence, 20 is the correct answer.

Get AI Help

Video Solution

video
View More Questions From Functions, Graphs and Statistics

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 41+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Simple Interest Compound Interest QuestionsCAT Averages QuestionsCAT Time, Speed and Distance QuestionsCAT Progressions and Series QuestionsCAT Time Speed Distance Questions

CAT DILR Questions | LRDI Questions For CAT

CAT DI with connected data sets QuestionsCAT Miscellaneous LR QuestionsCAT Quant Based LR QuestionsCAT Charts QuestionsCAT Selection With Condition Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Reading Comprehension QuestionsCAT Vocabulary QuestionsCAT Critical Reasoning QuestionsCAT Odd One Out QuestionsCAT Para Summary Questions

Free CAT Quant Questions

CAT InequalitiesCAT Quadratic EquationsCAT Data SufficiencyCAT Number SeriesCAT MiscellaneousCAT Simple Interest Compound InterestCAT AveragesCAT Time Speed DistanceCAT Coordinate GeometryCAT Logarithms, Surds and IndicesCAT Time And WorkCAT LogarithmsCAT Number SystemsCAT Time, Speed and DistanceCAT Linear EquationsCAT Probability, CombinatoricsCAT RemaindersCAT ArithmeticCAT Progressions and SeriesCAT AlgebraCAT Venn DiagramsCAT Averages Mixtures AlligationsCAT Profit And LossCAT Profit and LossCAT GeometryCAT MensurationCAT Functions, Graphs and StatisticsCAT PercentagesCAT Averages, Ratio and Proportion

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored
CAT mentor

Join CAT 2026 course by 5-Time CAT 100%iler

Start your IIM journey with the right preparation and crack CAT 2026.

Enroll Now
Ask AI