Let f(x)=1+2 x^2+2^2 x^4+…+2^10 x^20. Then, f(x) has

We have,

$f(x)=1+2 x^2+2^2 x^4+...+2^{10} x^{20}$

$\Rightarrow f'(x)=x\left(4+4 . 2^2 . x^2+...+20 . 2^{10} x^{18}\right)$

Clearly, f'(x) = 0 at x = 0 only and f''(0) > 0

Hence, f(x) has exactly one minimum.