Question

Consider g(x)=x³-x²-8 x+15 on the interval [-3,2] Since g is a polynomial, it is continuous and differentiable for all x , so it is continuous on [-3,2]

Answer 1

The question pertains to polynomial functions in Mathematics, discussing their continuity, differentiability, and related properties in the context of high school calculus.

Step-by-step explanation:

The subject of the question is Mathematics, specifically related to polynomial functions and their properties such as continuity and derivability. The question mentions a polynomial function g(x) defined on the interval [-3,2]. Polynomials are indeed continuous and differentiable on all real numbers, which means they do not have any breaks, holes, or sharp corners within their domain, and you can find a derivative for every point within this domain.

For example, the function f(x) mentioned as a horizontal line on the interval [0, 20] represents a special kind of polynomial, a constant function, which is also continuous across its domain. Additionally, the mention of properties like continuous probability functions and the integral of functions implies that the question might involve understanding areas under a curve, which is a basic concept within integration in calculus.