Question

Which of the graphs below represent the function f(x) = x3 - 5x2 + 2x + 8? You may sketch the graph to compare.

Answer 1

II graph is correct

Explanation:

Given are 4 graphs and we have to find out the match for

`f(x) = x^3 - 5x^2 + 2x + 8`

To find y intercept:

Put x=0

y intercept = 8. The second graph has this intercept

To find x intercept

Let f(x) =0 to get y intercepts

The given funciton has factors as

`(x+2)(x-1)(x-3)`

So x intercepts are -2, 1, 3 and this matches with II graph

Increasing:

`f'(x) = 3x^2-10x+2\\`

f'(x) =0 for x =0.214 and 3.12

OUr II graph has critical points at these values

SO option II is right

Answer 2

The answer in the attached figure

Explanation:

we have

`f(x)=x^(3)-5x^(2) +2x+8`

we know that

The y-intercept is the value of the function when the value of x is equal to zero

The x-intercept is the value of x when the value of the function is equal to zero

Using a graphing tool-------> Find the intercepts of the function

see the attached figure

The y-intercept is
`8`

The x-intercepts are
`-1,2,4`

therefore

the answer in the attached figure