) be a critical point of function f x
Chapter 1: Chapter 7 · MATHEMATICS-VOLUME 2 · EN medium
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( ) that is continuous on an open interval I containing c . If f x ( ) is differentiable on the interval, except possibly at c , then f c ( ) can be classified as follows:(when moving across I from left to right) (i) If ′ ( ) x changes from negative to positive at c , then f x ( ) has a local minimum f ( c ). (ii) If ′ ( ) x changes from positive to negative at c , then f x ( ) has a local maximum f ( c ). (iii) If ′ ( ) x is positive on both sides of c , or negative on both sides of c then f x ( ) has neither a local minimum nor a local minimum.
📖 Class 12 Mathematics English Volume 2 2025 Edition www.tntextbooks.in · Page 61
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( ) that is continuous on an open interval I containing c . If f x ( ) is differentiable on the interval, except possibly at c , then f c ( ) can be classified as follows:(when moving across I from left to right) (i) If ′ ( ) x changes from negative to positive at c , then f x ( ) has a local minimum f ( c ). (ii) If ′ ( ) x changes from positive to negative at c , then f x ( ) has a local maximum f ( c ). (iii) If ′ ( ) x is positive on both sides of c , or negative on both sides of c then f x ( ) has neither a local minimum nor a local minimum.
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