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21) The graph of the function f(x) = x3 - 2x2 + 4x – 8 intersects the x-axis at the point (2,0) as shown.
Which statement is true?

A) The function has 3 different zeros.

B) The function has 1 real zero that occurs 1 time.

C) The function has 1 real zero that occurs 2 times.

D) The function has 1 real zero that occurs 3 times.

21 The Graph Of The Function Fx X3 2x2 4x 8 Intersects The Xaxis At The Point 20 As Shown Which Statement Is True A The Function Has 3 Different Zeros B The Fu class=

Sagot :

MrRoyal

The true statement about the graph of the function f(x) = x3 - 2x2 + 4x – 8 is (B) The function has 1 real zero that occurs 1 time.

How to determine the true statement

The function of f(x) is represented as:

[tex]f(x)=x^3-2x^2+4x-8[/tex]

Differentiate the function f(x)

[tex]f'(x)=3x^2-4x+4[/tex]

Calculate the minimum value using:

[tex]x = -\frac b{2a}[/tex]

So, we have:

[tex]x = -\frac {-4}{2*3}[/tex]

[tex]x = \frac {2}{3}[/tex]

Substitute 2/3 in f'(x)

[tex]f'(2/3)=3*(2/3)^2-4(2/3)+4[/tex]

[tex]f'(2/3)=\frac 83[/tex]

The value of f'(2/3) is greater than 0.

This means that the function f(x) has 1 real zero, and it occurs once at point (2,0)

Hence, the true statement is (b)

Read more about functions at:

https://brainly.com/question/13136492

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