Question

hw3 defining the derivative (targets l6, d3; §3.1)
score: 0/5 answered: 0/5
question 3
if ( f(x)=\frac{6}{x^{2}} ), find ( f(3) )
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Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{6}{x^{2}}$ as $f(x) = 6x^{-2}$.

Step2: Apply the power - rule for derivatives

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. For $f(x)=6x^{-2}$, we have $a = 6$ and $n=-2$. So $f^\prime(x)=6\times(-2)x^{-2 - 1}=-12x^{-3}=-\frac{12}{x^{3}}$.

Step3: Evaluate $f^\prime(3)$

Substitute $x = 3$ into $f^\prime(x)$. So $f^\prime(3)=-\frac{12}{3^{3}}=-\frac{12}{27}=-\frac{4}{9}$.

Answer:

$-\frac{4}{9}$