10) AP Calculus linear functions

[karush]

$\textbf{10)} \\
f(x)\text{ is continuous at all } \textit{x}
\\
\displaystyle
f(0)=2, \, f'(0)=-3,\, f''(0)=0 $
$\text{let} \textbf{ g }
\text{be a function whose derivative is given by}\\
\displaystyle g'(x)=e^{-2 x} (3f(x))+2f'(x)
\text{ for all x}\\$
$\text{a) write an equation of the line tangent to the graph of f at the point where } $ $x=0$
$\displaystyle y-2 = -3(x-0) \\$
$\text{b) given that } \displaystyle g(0)=4, \\
\text{ write an equation of the line tangent of}
$g$
\text{at the point where }
\textit{x=0} \\$
$\displaystyle m_g=g'(0)=(1)[(3\cdot2)+2(0)]=6 \\
y-4=6(x-0)$

Was not sure about $g$ ??

 

[MarkFL]

For part b), check the slope of the tangent line. :)