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.

the answer is d

step-by-step explanation:

y+3=-4(x-2)

y+3=-4x+8

  -3         -3  

y=-4x+5

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it