Answer:
y = 4x + 4
Step-by-step explanation:
given :
y = 8 [tex]\sqrt{x}[/tex] , (1,8)
The equation for the tangent to the curve at the given point
y' = 8. ( [tex]( \frac{1}{2\sqrt{x} } ) = \frac{4}{\sqrt{x} }[/tex]
next calculate the slope of the tangent (m) = y' at x = 1 = 4
hence the equation of the tangent is
y - y' = m( x - x1 )
y - 8 = 4 ( x - 1 )
y = 4x + 4
attached below is the sketch of the curve and the tangent together
