# How do you Use implicit differentiation to find the equation of the tangent line to the curve #x^3+y^3=9# at the point where #x=-1# ?

##### 1 Answer

We begin this problem by finding the point of tangency.

**Substitute in the value of 1 for #x#.**

Not sure how to show a cubed root using our math notation here on Socratic but remember that raising a quantity to the

**Raise both sides to the #1/3# power**

We just found that when

**Complete the Implicit Differentiation**

**Substitute in those #x and y# values from above #=>(1,2)#**

Now use the slope intercept formula,

We have

We have

**Make the substitutions**

**Equation of the tangent line ...**

**To get a visual with the calculator solve the original equation for #y#.**