Question

find f(x).

f(x) = (x² - 7)(x² + 2)

f(x) =
(type an exact answer.)

Explanation:

Step1: Apply the product rule

The product rule states that if \(y = u\cdot v\), then \(y^\prime=u^\prime v + uv^\prime\). Let \(u = x^{2}-7\) and \(v=x^{2}+2\). First, find \(u^\prime\) and \(v^\prime\). Using the power rule \((x^{n})^\prime=nx^{n - 1}\), we have \(u^\prime=\frac{d}{dx}(x^{2}-7)=2x\) and \(v^\prime=\frac{d}{dx}(x^{2}+2)=2x\).

Step2: Substitute into the product rule formula

$$
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$$

Step3: Expand the expression

$$
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$$

Step4: Combine like - terms

$$
LATEXBLOCK2
$$

Answer:

\(4x^{3}-10x\)