Question

Which is the correct graph of f(x)=x^3-10x^2+9xThe pictures won’t sendNOTE: not the complete options. They are 4 in number

Answer 1

the roots of the function is 0, 1 and 9 (option D)

see graph below

Step-by-step explanation:

The given function:

`f\mleft(x\mright)=x^3-10x^2+9x`

We need to find the root of the function. The roots are the value of x when f(x) = 0

`\begin{gathered} 0=x^3-10x^2+9x \\ 0=x(x^2\text{ - 10x + 9)} \\ x\text{ = 0} \\ or\text{ }x^2\text{ - 10x + 9 = 0} \end{gathered}`
`\begin{gathered} x^2\text{ - 10 x + 9 = 0} \\ x^2\text{ -9x - x + 9 = 0} \\ x(x\text{ - 9) -1(x - 9) = 0} \\ (x\text{ - 1)(x - 9) + 0} \\ x\text{ - 1 = 0 or x -9 = 0} \\ x\text{ = 1 or x = 9} \end{gathered}`

So, the roots of the function is 0, 1 and 9

These are the points the line crosses the x axis.

We need to check for the graph whose line crosses he x axis at x = 0, x = 1 and x = 9 (option D)