AP EAMCET202317 May 2023Evening ShiftMathematicsApplication of DerivativesActual

If f(x)=3 x+ 12 x is continuous on R - 0 and M is its maximum value, then _ x M (f x)=

Options

A37
B-37
C2
D-2

Correct answer

B. -37

Step-by-step solution

f(x)=3 x+ 12 x f^ (x)=3- 12 x^2 For critical point: f^ (x)=0 aligned & 3- 12 x^2 =0 x^2=4 x=-2,2 & f^ (x)= 24 x^3 aligned At x=-2, f^ (-2)=-3 < 0 f(x) has maxima at x=-2 and maximum value is aligned & f(-2)=-6-6=-12 & M=-12 aligned _ x M f(x)= _ x -12 (3 x+ 12 x )=-37

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