Question

Math picture below...

Answer 1

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.

Answer 2

Explanation:

ans is c) f(x) is a polynominal function. The degree is 5 and the leading coefficient is -7.

x -> ∞, f(x) -> ∞; x -> -∞, f(x) -> -∞

the only ans that follows the above is a) f(x)=7x^9-3x^2-6

correct statments are: c) (1, 6.08) and (3, 0.75) are local extrema for the function and d) (-2, -9.67) is the global minimum for the function.