a. use the intermediate value theorem to show that the following equation has a solution on the given…

a. use the intermediate value theorem to show that the following equation has a solution on the given interval. b. use a graphing utility to find all the solutions to the equation on the given interval. c. illustrate your answers with an appropriate graph. 4x³ + x + 3 = 0; (-1,1) a. the intermediate value theorem states that if f is continuous on the interval a,b and l is a number strictly between f(a) and f(b), then there exists at least one number c in (a,b) satisfying f(c)=l. for which values of x is the function f(x)=4x³ + x + 3 continuous? a. it is continuous for all x. b. it is continuous on -1,1, but not for all x. c. it is continuous for some x, but not on -1,1. d. it is not continuous on any interval.

a. use the intermediate value theorem to show that the following equation has a solution on the given interval. b. use a graphing utility to find all the solutions to the equation on the given interval. c. illustrate your answers with an appropriate graph. 4x³ + x + 3 = 0; (-1,1) a. the intermediate value theorem states that if f is continuous on the interval a,b and l is a number strictly between f(a) and f(b), then there exists at least one number c in (a,b) satisfying f(c)=l. for which values of x is the function f(x)=4x³ + x + 3 continuous? a. it is continuous for all x. b. it is continuous on -1,1, but not for all x. c. it is continuous for some x, but not on -1,1. d. it is not continuous on any interval.

Answer

Answer:

A. It is continuous for all x.

Explanation:

Step1: Recall polynomial continuity

Polynomial functions $f(x)=a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0$ are continuous everywhere.

Step2: Identify function type

The function $f(x)=4x^{3}+x + 3$ is a polynomial function with $n = 3$, $a_3=4$, $a_1 = 1$, $a_0=3$ and other coefficients 0.

Step3: Determine continuity

Since it is a polynomial, it is continuous for all real - valued x.