4. Polynomial Functions

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x³−x−1; between 1 and 2

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x³−4x²+2; between 0 and 1

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=(3x-1)(x+2)²

In Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x⁴+6x³−18x²; between 2 and 3

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=(4x+3)(x+2)²

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = (x + 3)²

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x³+x²−2x+1; between -3 and -2

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=x³+5x²-x-5

Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4.

$\text{ƒ}\left(x\right)=x^3+x^2-36x-36$

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -(x - 2)² - 5

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=-x³+x²+2x

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=3x³−8x²+x+2; between 2 and 3

Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4.

$\text{ƒ}\left(x\right)=-3x^4-5x^3+2x^2$

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = x² - 4x + 3

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x³(x²-4)(x-1)