Answer:
Step-by-step explanation:
Given f(x) = 4 - 7x^5
Note the ^5 on x and the -7 in front of x^5
f(x) is a polynominal function. The degree is 5 and the leading coefficient is -7.
Given x -> ∞, f(x) -> ∞ and x -> -∞, f(x) -> -∞
Because (-x)^(2n) = x^(2n), the polynominal's degree cannot be an even number.
If the lead coefficient ax^n is negative, x -> ∞, f(x) -> -∞. So the lead coefficient cannot be negative.
Among the choice, the only correct answer is f(x) = 7x^9 - 3x^2 - 6
From the graph, the polynominal reaches its max at x=1 and mini at x=-2 and x=3.
Of the three extrema, only the one at x=-2 is the global mini while at x=3 is a local mini and at x=1 is a local max.
So the last two statements are correct.
