Question 60232
Find the equation of the tangent line to the curve y=e^3x at the point (0,1)

To make the equation of a line, we need both a slope and a point.  We find the slope of a tangent line by taking the derivative of the function and pluging in your point.
{{{y=e^(3x)}}}
y'={{{e^(3x)*(3)}}}
y'={{{3e^(3x)}}}
m=y'(0)={{{3e^(3*0)}}}
m=y'(0)={{{3e^(0)}}}
m=y'(0)={{{3(1)}}}
m=y'(0)=3
Since they gave us the y-intercept as a point we can use the slope-intercept formula to make the equation of the line: {{{highlight(y=mx+b)}}}, m=slope, (0,b)=y-intercept.
m=3 and (0,b)=(0,1)
{{{highlight(y=3x+1)}}}
Happy Calculating!!!