Question

An equation of the line tangent to y=x^3+3x^2+2 at its point of inflection is

Answer 1

Answer:

y = 2

y = 6

Step-by-step explanation:

The first thing to do is to find the turning point of the function. For this, derive and equal zero to expression

$\frac{\delta y}{\delta x}$ = $3x^2 +6x$

$\frac{\delta y}{\delta x} = 0$

$3x^2 +6x = 0$

$3x(x +2) = 0$

x = 0 and  x = -2

We have 2 inflection points.

Then we have 2 tangent lines:

At the point (0, 2)

Since it is a point of inflection, then the slope of this line is 0. Therefore the tangent line is:

y = 2.

At the point (-2, 6).

The slope of this line is 0.

The equation of the tangent line to the function is:

y = 6