Find-minimum-value-of-function-f-x-2x-x-1-x-2-1-

Question Number 167167 by cortano1 last updated on 08/Mar/22

Find minimum value of function

f (x) = 2 x - \sqrt{x + 1} - \sqrt{x^{2} - 1}

Answered by MJS_new last updated on 08/Mar/22

f (- 1) = - 2

f has a singularity at x = - 1

Commented by cortano1 last updated on 08/Mar/22

not minimum value = \frac{1}{4} ?

Commented by cortano1 last updated on 08/Mar/22

when x = \frac{5}{4}

Commented by MJS_new last updated on 08/Mar/22

yes {there}^{'} s a local minimum at x = \frac{5}{4}

but the absolute minimum is at x = - 1

Commented by cortano1 last updated on 09/Mar/22

no sir since D_{f} is x ⩾ 1

Commented by MJS_new last updated on 09/Mar/22

no . {it}^{'} s defined for x = - 1 \lor x ⩾ 1

f (- 1) = 2 \times (- 1) - \sqrt{- 1 + 1} - \sqrt{{(- 1)}^{2} - 1} =

= - 2 - \sqrt{0} - \sqrt{0} = - 2

Facebook Tweet Pin