Question

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Answer 1

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:

$f(x)=x^3-2x^2+4x-8$

Differentiate the function f(x)

$f'(x)=3x^2-4x+4$

Calculate the minimum value using:

$x = -\frac b{2a}$

So, we have:

$x = -\frac {-4}{2*3}$

$x = \frac {2}{3}$

Substitute 2/3 in f'(x)

$f'(2/3)=3*(2/3)^2-4(2/3)+4$

$f'(2/3)=\frac 83$

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)

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