Mathematics - Calculus
Calculus GATE Syllabus
Calculus: Limits, continuity and differentiability. Maxima and minima. Mean value theorem. Integration
2. The function f(x) = x3 - 6x2 + 9x + 25 has
4. The interval in which the Lagrange's theorem is applicable for the function f(x) = 1/x is
- Option : C
- Explanation : Since f(x) = (1/x) is not continuous in [- 3, 3] [- 4, 2] or [- 1, 1], The point of discontinuity is '0'. Only in [2, 3] the function is continuous, and differentiable hence mean value theorem is applicable in [2, 3].
5. If f(x) = | x | , then for interval [-1, 1] ,f(x)
- Option : C
- Explanation : Since f(x) = |x| is continuous in [-1, 1] but it is not differentiable at x = 0 ε (-1, 1)
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