Question

Find the slope of the tanget line ?

Answer 1

The slope of the tangent is `-1/6`.

Explanation:

Slope of the tangent at a given point on the curve `f(x)` is given by `f'(x_0)`.

As `f(x)=sqrt(8-x)`

`f'(x)=1/(2sqrt(8-x))xxd/(dx)(8-x)`

= `(-1)/(2sqrt(8-x))`

As such the slope of the tangent is

`f'(-1)=(-1)/(2sqrt(8-(-1)))=-1/6`

Additionally as `f(-1)=3`, equation of tangent is

`y-3=-1/6(x+1)` or `x+6y-17=0`

and tangent appears as follows:

graph{(y-sqrt(8-x))(x+6y-17)=0 [-25, 15, -5, 15]}