Let the function  f:−7,0→R be continuous on  −7,0and differentiable on −7,0. If  f−7=−3and  f'x≤2 for all such function f, f−1+f0 is in the interval:

Lets use LMVT for x∈−7,−1  f−1−f−7−1+7=f'x≤2 ⇒f−1+36≤2 ⇒f−1≤9   →1                                    Also use LMVT forx∈−7,0  f0−f−70+7=f'x≤2⇒f0+37≤2 ⇒f0≤11   →2 Adding 1 and 2, we get            ∴f0+f−1≤20