Find the slope of the tanget line ?

Question

2454 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-18T17:13:04

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

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]}