Question 1183580

Let {{{f(x)=(5/2)x^2-e^x}}} . 

Find the value of {{{x}}} for which the second derivative {{{f}}}''{{{(x )}}} equals zero.

{{{f(x)=(5/2)x^2-e^x }}}....first find first derivate

{{{f}}} ‘{{{(x)= 5x - e^x}}}

now find second derivate

{{{f}}}‘‘{{{(x)= 5 - e^x}}}


second derivative {{{f}}}''{{{(x )}}} equals zero:

{{{5 - e^x=0}}}

{{{5 =e^x}}}..........take natural log of both sides

{{{ln(e^x)=ln(5)}}}

{{{x*ln(e)=ln(5)}}}............{{{ln(e)=1}}}

{{{x=ln(5)}}}