Question

If f(x) =x^3 -2x^2 -3x -6 over [-1,4] then find 'c' using LMVT​

Answer 1

Answer:

Since, f(x) = x2 – 2x + 4 is a polynomial. So, f(x) is continuous on [1,5] and differentiable on (1,5) Now, f ' (x) = 2x – 2 and f (1) = 1 – 2 + 4 = 3 f (5) = 25 – 10 + 4 = 19 By Lagrange's mean value theorem, there exists c ∈ (1,5) such that => 2C = 6 . .. C = 3 ∈ (1, 5) Hence, Lagrange's mean value theorem is  verify-lagranges-mean-value-theorem-for-the-function-f-x-x-2-2x-4-on-1-5