JEE Main2013MathematicsApplication of DerivativesActual

Let f(1)=-2 and f^ (x) 4.2 for 1 x 6 . The possible value of f(6) lies in the interval :

Options

A[15,19)
B(- , 12)
C[12,15)
D[19, )

Correct answer

D. [19, )

Step-by-step solution

Given f(1)=-2 and f^ (x) 4.2 for 1 x 6 Consider f^ (x)= f(x+h)-f(x) h f(x+h)-f(x)=f^ (x) h (4.2) h So, f(x+h) f(x)+(4.2) h put x=1 and h=5 , we get f(6) f(1)+5(4.2) f(6) 19 Hence f(6) lies in [19, )

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