An equation of the line tangent to y=x3+3x2+2 at its point of inflection is A. y=−6x−6y is equal to negative 6 x minus 6

B. y=−3x+1y is equal to negative 3 x plus 1

C. y=2x+10y is equal to 2 x plus 10

D. y=3x−1

Explanation:

Given

Required

Determine the equation at the point of inflection

The point of inflection of a curve is the point where the second derivative is 0.

So:

First derivative is:

Second derivative:

Equate to 0

Solve for x

Next, we calculate the slope (m) of the point using the first derivative.

Substitute -1 for x in

To get the y equivalent;

Substitute in

Lastly, we calculate the line equation using:

Where

and

So, we have:

Make y the subject

Hence, the equation is: