Question

self-assessment
1 i dont understand yet 2 i can do it with help 3 i can do it on my own. 4 i can teach someone else.
evaluate the function for the given value of x.

1. $f(x) = -x^3 + 3x^2 + 9; x = 4$
2. $f(x) = 3x^5 - x^4 - 6x + 10; x = -2$

Explanation:

Step1: Substitute \(x = 4\) into \(f(x)=-x^{3}+3x^{2}+9\)

$$\begin{align*} f(4)&=-(4)^{3}+3\times(4)^{2}+9\\ &=-64 + 3\times16+9 \end{align*}$$

Step2: Calculate the value

$$\begin{align*} f(4)&=-64+48 + 9\\ &=-16+9\\ &=-7 \end{align*}$$

Step3: Substitute \(x=-2\) into \(f(x)=3x^{3}-x^{4}-6x + 10\)

$$\begin{align*} f(-2)&=3\times(-2)^{3}-(-2)^{4}-6\times(-2)+10\\ &=3\times(-8)-16 + 12+10 \end{align*}$$

Step4: Calculate the value

$$\begin{align*} f(-2)&=-24-16+12 + 10\\ &=-40+22\\ &=-18 \end{align*}$$

Answer:

For \(f(x)=-x^{3}+3x^{2}+9\) when \(x = 4\), \(f(4)=-7\). For \(f(x)=3x^{3}-x^{4}-6x + 10\) when \(x=-2\), \(f(-2)=-18\).