99 Percentile Qs Bank for JEE MainMathematicsApplication of Derivatives

If f:[2,3] R is defined by f(x)=x^3+3 x-2 , then the range f(x) is contained in the interval

Options

A[1,12]
B[12,34]
C[35,50]
D[-12,12]

Correct answer

B. [12,34]

Step-by-step solution

Given, f(x)=x^3+3 x-2 On differentiating w.r.t. x , we get aligned & f^ (x)=3 x^2+3 & Put f^ (x)=0 3 x^2+3=0 & x^2=-1 & f(x) is either increasing or decreasing. & At x=2, f(2)=2^3+3(2)-2=12 & At x=3, f(3)=3^3+3(3)-2=34 & f(x) [12,34] . aligned

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