GATE 2021 CS (CS2) – Question 35

Engineering Mathematics · Calculus · 1 mark · Numerical answer

f is continuous on [−3,3] and differentiable on (−3,3), with f′(x)≤2. If f(−3)=7, find the greatest possible f(3).

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Correct answer: 19 to 19

Explanation

The mean-value theorem gives f(3)−f(−3)=6f′(c)≤12 for some interior c. Hence f(3)≤7+12=19. Equality is attainable with the linear function f(x)=2x+13, so nineteen is the greatest possible value.

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