Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1) (astroid)

Applying implicit differentiation, the equation of the tangent line is given by:

The equation of a line tangent to a function f(x) at a point is given by:

In this problem, point , thus

The function is:

To find the derivative, we have to apply implicit differentiation, thus:

Thus:

Then, the equation to the line tangent is:

A similar problem is given at link

Answer with Step-by-step explanation:

We are given that an equation of curve

We have to find the equation of tangent line to the given curve at point

By using implicit differentiation, differentiate w.r.t x

Using formula :

Substitute the value x=

Then, we get

Slope of tangent=m=

Equation of tangent line with slope m and passing through the point is given by

Substitute the values then we get

The equation of tangent line is given by

This is required equation of tangent line to the given curve at given point.

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.