If `H(x_(0))`=0 for some x=`x_(0)`and `(d)/(dx)H(x)gt2cxH(x)` for all `xgex_(0)`where `cgt0` then

Options

A. H(x) = 0 has root for `x gt x_(0)`
B. H(x) = 0 has no root for `x gt x_(0)`
C. H(x) is a constant functio
D. none of these

Answer

2

Explanation

Given that `(d)/(dx)H(x)gt2cxH(x)`
or `e^(-cx^(2))(d)/(dx)H(x)-e^(-cx^(2))2cxH(x)gt0`
or `(d)/(dx)H(x)e^(-cx^(2))gt0`
Thus `H(x)e^(-cx^(2))` is and increasing function
But `h(x_(0))gt0` for all `xgtx_(0)`
Hence H(x) connot be zero for any `xgtx_(0)`