Question

Ffind an equation for the tangent to the curve at the given point. Then sketch the curve and the tangent together.

Answer 1

Answer:

y = 4x + 4

Step-by-step explanation:

given :

y = 8 $\sqrt{x}$ , (1,8)

The equation for the tangent to the curve at the given point

y' = 8. ( $( \frac{1}{2\sqrt{x} } ) = \frac{4}{\sqrt{x} }$

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