Hei!
Denna oppg. sliter eg litt med.
Bestem konstanten p slik at g'(4)=1 da g(x)=1/(px)+ [symbol:rot] x
Fasit: p=-(1/12)
g(x)=1/(px)+ [symbol:rot] x
g'(x)=((1*1*p)-(0*p*x)+(0.5x^-0.5)) / (px)^2
som gir,
(1/(px^2))+0.5x^-0.5
g'(4)=1 gir,
1=(1/(p*4^2))+0.5*4^-0.5
p=(1/(1*4^2))+2^-0.5
1/16+2^-0.5
Her tar det stopp ... )))
Likning som suger ...
Moderatorer: Aleks855, Gustav, Nebuchadnezzar, Janhaa, DennisChristensen, Emilga
[tex] g(x) = \frac{1}{px} + \sqrt{x} [/tex]
[tex] \frac{dg(x)}{dx} = -\frac{1}{px^2} + \frac{1}{2\sqrt{x}} [/tex]
[tex] \frac{dg(4)}{dx} = 1 = -\frac{1}{16p} + \frac{1}{4} [/tex]
[tex] p(1-\frac{1}{4}) = -\frac{1}{16} [/tex]
[tex] p = \frac{-\frac{1}{16}}{1-\frac{1}{4}} = -\frac{1}{12} [/tex]
[tex] \frac{dg(x)}{dx} = -\frac{1}{px^2} + \frac{1}{2\sqrt{x}} [/tex]
[tex] \frac{dg(4)}{dx} = 1 = -\frac{1}{16p} + \frac{1}{4} [/tex]
[tex] p(1-\frac{1}{4}) = -\frac{1}{16} [/tex]
[tex] p = \frac{-\frac{1}{16}}{1-\frac{1}{4}} = -\frac{1}{12} [/tex]