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Maths-

General

Easy

Question

Suppose that $f$ is differentiable for allx and that $f to the power of ’ end exponent left parenthesis x right parenthesis less or equal than 2$ for all x If $f left parenthesis 1 right parenthesis equals 2$ and f(4)=8 then f(2) has the value equal to

$3$
$4$
$6$
8

The correct answer is: $4$

In the question it is given that f is differentiable to solve lets use Lagranges mean value theorem innn the interval [1,4]
f'(c)= f(4)-f(1)/3
f'(c)=2
f'(x)=2
f(x)=2x+4
f(1)=2+k
k=0
f(x)=2x
f(2)=4

Hence f(2)=4 is the suitable option

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