IGNOU BMTC 131 2026 - Verigy Lagrange's mean value theorem for the function f defined by

Question

Verigy Lagrange's mean value theorem for the function f defined by

$f(x) = 2x^2 - 7x - 10$ over [2, 5].

09 Jan 2026

Answer :

Word Count : 186

The function is given by f(x) = 2x² − 7x − 10. Being a polynomial function, f(x) is continuous on the closed interval [2, 5] and differentiable on the open interval (2, 5). Hence all the conditions of Lagrange’s mean value theorem are satisfied. According to the theorem, there exists at least one real number c in (2, 5) such that f′(c) = [f(5) −

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