4. Find an equation of the line that is tangent to the graph of 4x + 2xy^2 +44 = y^3 at the point (-3,2). i need this asap.

Given:

The equation is:

To find:

The equation of the tangent on the given equation at point (-3,2).

Solution:

We have,

Differentiate with respect to x.

Isolate y'.

Now, we need to find the value of the derivative at point (-3,2).

It means the slope of the tangent line is .

The equation of tangent line that passes through the point (-3,2) with slope is:

Therefore, the equation of tangent line is .

d. all of the above

step-by-step explanation: