Question

The value of c of Lagrange's mean value theorem for f (x) = xsquare - 3x+2 in [-2,3] is

Answer 1

Answer:

Given function f(x) = x2 – 3x + 2, x ∈ [- 2, 3] Clearly,f(x) is continuous in interval [-2, 3] and f'(x) is finite and exists in (-2, 3). So, f(x) is differentiable in (- 2, 3). Hence f(x) satisfies both conditions of Langrange’s mean value theorem. Read more on Sarthaks.com - https://www.sarthaks.com/710175/verify-the-lagranges-mean-value-theorem-for-the-following-functions-i-f-x-x-2-3x-2-x-2-3

Step-by-step explanation:

Thus, langrange's mean value theorem satisfied. (ii) Given function f(x) = 1/(4x - 1), x ∈ [1, 4] Clearly,f(x) is continuous in [ 1,4] and f'(x) is finite and exist in interval (1,4). Hence,f(x) is differentiable in (1, 4). f(x) satisfies both conditions of Langrange’s mean value theorem. Read more on Sarthaks.com - https://www.sarthaks.com/710175/verify-the-lagranges-mean-value-theorem-for-the-following-functions-i-f-x-x-2-3x-2-x-2-3

Thus, Langrange’s mean value theorem satisfied.Read more on Sarthaks.com - https://www.sarthaks.com/710175/verify-the-lagranges-mean-value-theorem-for-the-following-functions-i-f-x-x-2-3x-2-x-2-3