The minimum value of $2^{(x^2-3)^3+27}$ equals:

$3^{27}$ $2^{27}$ 1 None of these

1

$(x^2-3)^3+27$ $f(x)=2$ $\log f(x)=(\log 2)((x^2-3)^3+27)$ differentiating wrt x $\frac{1}{f(x)}f'(x)=3(x^2-2)^2×2x\log 2$ so $f'(x)=2^{(x^2-3)^3+27}×6(x^2-3)^2.x$ $f'(x)$ changes sign at $x=0$ from "-" to "+" so min value is at x = 0 $f(0)=2^0=1$