Question

exercsies 3.3 differentiation rules
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question 3
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if (f(x)=\frac{3}{x^{2}}), find (f(3)).
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Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{3}{x^{2}}$ as $f(x)=3x^{- 2}$.

Step2: Apply the power - rule for differentiation

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

Step3: Evaluate $f^\prime(x)$ at $x = 3$

Substitute $x = 3$ into $f^\prime(x)$. So $f^\prime(3)=-\frac{6}{3^{3}}=-\frac{6}{27}=-\frac{2}{9}$.

Answer:

$-\frac{2}{9}$