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प्रश्न
Verify Mean Value Theorem, if f (x) = x3 – 5x2 – 3x in the interval [a, b], where a = 1 and b = 3. Find all c ∈ (1, 3) for which f ′(c) = 0.
उत्तर
The given function f is f (x) = x3 – 5x2 – 3x
f, being a polynomial function, is continuous in [1, 3] and is differentiable in (1, 3) whose derivative is 3x2 − 10x − 3.
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