Home > Calculus > Tangent Line to a Curve

Find the slope of the tanget line ?

Answer 1

Scarlett Allison

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]}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Adam Adkins

To find the slope of a tangent line, you need to know the equation of the curve at the point where the tangent line touches it. Once you have the equation, you can find the derivative of the curve with respect to the variable. The derivative will give you the slope of the tangent line at that point.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.