Suppose f: R -- R is a continuous function on [-3, 3] and differentiable on (-3, 3) such that for e

Q: What is GATE-CS?

GATE-CS is a competitive examination conducted in India. This question is from the 2021 GATE-CS Engineering Mathematics paper.

Q: How can I prepare for GATE-CS Engineering Mathematics?

To prepare for GATE-CS Engineering Mathematics, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2021 question covers Mean Value Theorem topic.

Q: What is the difficulty level of this question?

This GATE-CS 2021 Engineering Mathematics question has a easy difficulty level and is marked as an important question.

Q: Where can I find more GATE-CS previous year questions?

You can find more GATE-CS previous year questions on AspirantMitraa. Browse by subject, topic, year, and difficulty level to practice effectively.

Question

Suppose f: R --> R is a continuous function on [-3, 3] and differentiable on (-3, 3) such that for every x in the interval, f'(x) <= 2. If f(-3) = 7, then f(3) is at most ___

Accepted Answer

Answer: 19Concept -- Mean Value Theorem (from Calculus by Thomas and Finney; Stewart Calculus):By the Mean Value Theorem, for a function continuous on [a,b] and differentiable on (a,b), there exists c in (a,b) such that f'(c) = [f(b) - f(a)] / (b - a).Here a = -3, b = 3, so b - a = 6. We know f'(x) <= 2 for all x in (-3, 3).Since f'(c) = [f(3) - f(-3)] / 6 and f'(c) <= 2:[f(3) - 7] / 6 <= 2. f(3) - 7 <= 12. f(3) <= 19.The maximum value of f(3) is attained when f'(x) = 2 throughout, giving f(3) = 7 + 2*6 = 19.

Suppose f: R --> R is a continuous function on [-3, 3] and differentiable on (-3, 3) such that for every x in the interval, f'(x) <= 2. If f(-3) = 7, then f(3) is at most ___

Master GATE-CS with Our Test Series

Frequently Asked Questions

Suppose f: R --> R is a continuous function on [-3, 3] and differentiable on (-3, 3) such that for every x in the interval, f'(x) <= 2. If f(-3) = 7, then f(3) is at most ___

Master GATE-CS with Our Test Series

Frequently Asked Questions

Suppose f: R --> R is a continuous function on [-3, 3] and differentiable on (-3, 3) such that for every x in the interval, f'(x) &lt;= 2. If f(-3) = 7, then f(3) is at most ___

Master GATE-CS with Our Test Series

Frequently Asked Questions

Suppose f: R --> R is a continuous function on [-3, 3] and differentiable on (-3, 3) such that for every x in the interval, f'(x) &lt;= 2. If f(-3) = 7, then f(3) is at most ___

Master GATE-CS with Our Test Series

Frequently Asked Questions

Suppose f: R --> R is a continuous function on [-3, 3] and differentiable on (-3, 3) such that for every x in the interval, f'(x) <= 2. If f(-3) = 7, then f(3) is at most ___

Suppose f: R --> R is a continuous function on [-3, 3] and differentiable on (-3, 3) such that for every x in the interval, f'(x) <= 2. If f(-3) = 7, then f(3) is at most ___