We are given function F(x) = x^3 +3x^2.
Leading term is the term that has highest power of a variable.
For the given function we have highest power 3 of x.
Therefore, leading term is x^3. We don't have any sign in front of x^3. Therefore, it's a positive leading term.
And degree of the is highest power, that is 3.
Therefore, degree is an odd number.
According to problem, we need to make the leading term as a negative number.
So, we need to find a rule for end behaviour of the graph with:
Leading coefficent = Negative.
Degree : Odd.
Please note the rule, when leading coefficent a negative number and degree is odd.
x--> + ∞ f(x) ---> - ∞
x--> - ∞ f(x) ---> + ∞
We can see option D has f(x) ---> - ∞ for x--> + ∞ and f(x) ---> + ∞ for x--> - ∞.
Therefore, correct option is D.
