Question

graph the function $f(x) = x^3 - 4x - 1$. which are approximate solutions for $x$ when $f(x) = 0$? select three options.
$\square$ $-2.11$
$\square$ $-1.86$
$\square$ $-0.25$
$\square$ $0.25$
$\square$ $2.11$

Explanation:

Step1: Evaluate f(-2.11)

Substitute \( x = -2.11 \) into \( f(x)=x^{3}-4x - 1 \).
\( f(-2.11)=(-2.11)^{3}-4\times(-2.11)-1\)
\(= - 9.393931+8.44 - 1=-1.953931\approx - 1.95
eq0\)

Step2: Evaluate f(-1.86)

Substitute \( x=-1.86 \) into \( f(x)=x^{3}-4x - 1 \).
\( f(-1.86)=(-1.86)^{3}-4\times(-1.86)-1\)
\(=-6.320576 + 7.44-1 = 0.119424\approx0.12\approx0\) (close to 0)

Step3: Evaluate f(-0.25)

Substitute \( x = - 0.25 \) into \( f(x)=x^{3}-4x - 1 \).
\( f(-0.25)=(-0.25)^{3}-4\times(-0.25)-1\)
\(=-0.015625 + 1-1=-0.015625\approx - 0.02\approx0\) (close to 0)

Step4: Evaluate f(0.25)

Substitute \( x = 0.25 \) into \( f(x)=x^{3}-4x - 1 \).
\( f(0.25)=(0.25)^{3}-4\times(0.25)-1\)
\(=0.015625-1 - 1=-1.984375
eq0\)

Step5: Evaluate f(2.11)

Substitute \( x = 2.11 \) into \( f(x)=x^{3}-4x - 1 \).
\( f(2.11)=(2.11)^{3}-4\times(2.11)-1\)
\(=9.393931-8.44 - 1=-0.046069\approx - 0.05\approx0\) (close to 0)

Answer:

-1.86, -0.25, 2.11