GATE 2022 MN – Question 42
A continuous differentiable function on [3, 18] satisfies f(3)=−50 and f′(x)≤20. Find the greatest possible f(18), as an integer.
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Correct answer: 250 to 250
Explanation
Integrate the derivative bound over the interval: f(18)−f(3)≤20(18−3)=300. Therefore f(18)≤−50+300=250. Equality is achieved by f(x)=−50+20(x−3), which has derivative exactly 20 throughout, so 250 is attainable.