Question

Find the equation of the tangent line to the curve y=11xex at the point (0,0). the equation of this tangent line can be written in the form y=mx
b. find m and
b.

Answer 1

$y=11xe^x\implies y'=11e^x(x+1)$

When $x=0$, the slope of the tangent line is $11e^0(0+1)=11$. The equation of the tangent line in point-slope form is then

$y-0=11(x-0)\implies y=11x$