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Tangent lines Find an equation of the line

Chapter 8, Problem 29RE

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QUESTION:

Tangent lines Find an equation of the line tangent to the following curves at the given point. Check your work with a graphing utility.

\(y^{2}=-12 x \); \(\left(-\frac{4}{3},-4\right)\)

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QUESTION:

Tangent lines Find an equation of the line tangent to the following curves at the given point. Check your work with a graphing utility.

\(y^{2}=-12 x \); \(\left(-\frac{4}{3},-4\right)\)

ANSWER:

Solution 29RE

Step 1:

In this  problem we have to find the equation  of the line tangent to  , at the  point ( - , -4).

First  let us  find the slope of  

Differentiate both sides with respect to x,  

                 ()

                 2y= -12 (x)

                  2y = -12 , since  

                        =  =

Therefore , slope of  is ; .

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