Question

the c of lagranges mean value theorem for the function f(x) = x^2 + 2x -1;a=0b= 1​

Answer 1

Answer:

f'(x) = 2x+2

f'(c) = 2c + 2 ........ (i)

now f(1) = 1+2–1 = 2, and f(0) = –1

so according to LMVT,

$2c + 2 = \frac{2 + 1}{1 - 0} = 3 \\ 2c = 1 \\ c = \frac{1}{2}$

ans