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

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

=

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

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.