V(x)=x^3 -3x^2-4x.Let x,x+1,and x-4 represent the width, the length, and the height respectively. The container has a volume of 70 ft^3.Find the container dimensions.

Question

The volume V of a container is modeled by the function V(x)=x^3 -3x^2-4x.Let x,x+1,and x-4 represent the width, the length, and the height respectively. The container has a volume of 70 ft^3.Find the container dimensions.

Answer 1

the solution is between 5.75-5.8

are you sure the volume is 70 ft³?

70 factors into 2 times 5 times 7, none of which could be x

Answer 2

The given function has one real root, 5.7840..., and two complex root.

Is the post accurate?

Answer 3

The goal is to solve the equation V(x) = 70.

x³ - 3x² - 4x = 70

x³ - 3x² - 4x - 70 = 0

Unfortunately the answer you'll get is not a rational number. You can verify this by plugging in all possible rational roots from the Rational Root Theorem.

A possible way to solve for the irrational root is to graph the function and find the x-intercept(s).

https://www.desmos.com/calculator/o6dap2ef6j

The graph in the link shows that the x-intercept is x=5.784

Therefore the dimensions are

x = 5.784

x+1 = 6.784

x-4 = 1.784

Check: 5.784 * 6.784 * 1.784 = 70.002 (rounded to 70)