Question

JEE mains and advance question .(AOD)

Let f(X) be a differentiable function such that f'(x)
$\leqslant 2$
X€R, If f(1)= 2 , f(4) = 8 then find f(2) ​

Answer 1

Step-by-step explanation:

Apply l.M.V.T in [1,2]

f(2) - f(1)/2-1 = f'(c)

$\leqslant 2$

f(2) - 2/1

$\leqslant 2$

f(2)

$\leqslant 4$

Apply l.M.V.T in (2,4)

f(4)-f(2)/4-2 = f'(c2)

$\leqslant 2$

8-f(2)/2

$\leqslant 2$

f(2)

$\geqslant 4$

since, f(2)

$\geqslant 4$

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Hope it helps !