using the sign chart for f(x)=x^3(x - 4)^2(x + 4)^2, and only that sign chart, what conclusions can be drawn…

using the sign chart for f(x)=x^3(x - 4)^2(x + 4)^2, and only that sign chart, what conclusions can be drawn about the graph of f on the interval 0 < x < 4? answer it is positive it is negative it is increasing it is decreasing it is concave up it is concave down none of the above

using the sign chart for f(x)=x^3(x - 4)^2(x + 4)^2, and only that sign chart, what conclusions can be drawn about the graph of f on the interval 0 < x < 4? answer it is positive it is negative it is increasing it is decreasing it is concave up it is concave down none of the above

Answer

Explanation:

Step1: Analyze the factors on the interval

On the interval (0 < x<4), consider (f''(x)=x^{3}(x - 4)^{2}(x + 4)^{2}). The factor ((x - 4)^{2}\geq0) and ((x + 4)^{2}>0) for all real - x. Also, for (0 < x<4), (x^{3}>0).

Step2: Determine the sign of (f''(x))

Since (x^{3}>0), ((x - 4)^{2}\geq0), and ((x + 4)^{2}>0) on the interval (0 < x<4), then (f''(x)=x^{3}(x - 4)^{2}(x + 4)^{2}>0) on the interval (0 < x<4).

Answer:

it is positive