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
[tex]\frac{\delta y}{\delta x}[/tex] = [tex]3x^2 +6x[/tex]
[tex]\frac{\delta y}{\delta x} = 0[/tex]
[tex]3x^2 +6x = 0[/tex]
[tex]3x(x +2) = 0[/tex]
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
