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Suppose that f is differentiable for all x and that f ′(x) ≤ 2 for all x. If f(1) = 2 and f(4) = 8, then f(2) has the value equal to………
Given f'(x)<=2 Integrate both side, we'll get f(x)=2x+C From Given , f(1)=2(1)+C=2 We Get C=0; Also F(4)=2(4)+0 = 8 (Given) Thus F(2)=2(2)=4 Please Reply if i am Wrong.
Given f'(x)<=2
Integrate both side, we'll get f(x)=2x+C
From Given , f(1)=2(1)+C=2
We Get C=0;
Also F(4)=2(4)+0 = 8 (Given)
Thus F(2)=2(2)=4
Please Reply if i am Wrong.
Using LMVT for f in [1, 2]2 1(2) (1)−f − f = f ′(c) ≤ 2 ⇒ f (2) – f (1) ≤ 2⇒ f(2) ≤ 4Using LMVT for f in [2, 4]4 2(4) (2)−f − f = f ′(d) ≤ 2 and proceed
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