Answer
The equation of the tangent is $y=-25x+4.$
Work Step by Step
Product Rule $(f’(x)=(u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$
$u(x)=(x-4) ;u’(x)=1 $
$v(x)= x^2+6x-1;v’(x)=2x+6 $
$f'(x)=(1)(x^2+6x-1)+(2x+6)(x-4)=3x^2+4x-25.$
$f'(0)=3(0^2)+4(0)-25=-25.$
Equation of tangent:
$(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$.
$(y-4)=-25(x-0)\rightarrow y=-25x+4.$
