Mean Value Theorems — Important Questions
ICSE · Class 12 · Mathematics
105 important questions from Mean Value Theorems for ICSE Class 12 Mathematics, with answers. Includes mcq and multiple choice questions.
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Important Questions from Mean Value Theorems
Rolle's Theorem guarantees the existence of c ∈ (a,b) such that:
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f'(c) = 0
The conclusion of Rolle's Theorem is that f'(c) = 0 for some c in the open interval (a,b).
How many conditions does Rolle's Theorem require?
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3
Three conditions: (i) f continuous on [a,b], (ii) f differentiable on (a,b), (iii) f(a) = f(b).
Lagrange's MVT does NOT require which of the following?
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f(a) = f(b)
LMVT only requires continuity on [a,b] and differentiability on (a,b). The condition f(a)=f(b) is needed only for Rolle's Theorem.
The conclusion of LMVT is:
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f'(c) = [f(b)-f(a)]/(b-a)
LMVT states f'(c) = [f(b)-f(a)]/(b-a) for some c ∈ (a,b). This equals the slope of chord AB.
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