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

  1. 3    
  2. 4    
  3. 6    
  4. 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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