Which of the following graphs could be the graph of the function f(x) = x4 + x3 – x2 – x?

The given function is ⇒ f(x) = x⁴ + x³ – x² – x

To graph the function, we need to find zeros, minimum and maximum points.

The zeros of the function can be obtained as following;

f(x) = x⁴ + x³ – x² – x = (x⁴ + x³) – (x² + x) = x³ (x+1) - x (x+1) = (x+1) (x³ - x)

∴ f(x) = (x+1) x ( x² - 1) = x (x+1) (x+1) (x-1) = x (x-1) (x+1)²

So, the zeros will be at x = 0 , 1 , -1

To find the minimum and maximum points, we need to get f'(x)

∴ f'(x) = 4x³ + 3x² - 2x - 1

solve for x when f'(x) = 0 using the calculator.

∴ x = -1 , -0.39 , 0.64

Making a table between x and f(x) with taking the zeros and minimum and maximum points into considerations.

So, the graph of f(x) will be as the attached figure.

answer: 12

step-by-step explanation:

7

step-by-step explanation:

the answer would be 7