Question

if f(x)=x^3 - 4x + 6, show that there are values c for which f(c) equals (a) π, (b) -√3, and (c) 5,000,000. does a solution exist between 165 and 170 for f(x)=5,000,000? inconclusive, because 5,000,000 does not lie between f(165) and f(170). yes, because f(165)>5,000,000>f(170). inconclusive, because f(165)<0 but f(170)>0. yes, because f(165)<5,000,000<f(170). so, continue using larger values of x. find f(175). f(175)= (simplify your answer.)

Explanation:

Step1: Recall the function

The function is $f(x)=x^{3}-4x + 6$.

Step2: Calculate $f(175)$

Substitute $x = 175$ into the function:
\[

$$\begin{align*} f(175)&=(175)^{3}-4\times175 + 6\\ &=175\times175\times175-700 + 6\\ &=5359375-700+6\\ &=5358681 \end{align*}$$

\]

Answer:

$5358681$