Final answer to the problem
$f\left(x\right)=\frac{\sin\left(2x\right)}{2}-x^2$
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Step-by-step Solution
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- Write in simplest form
- Solve by quadratic formula (general formula)
- Find the derivative using the definition
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
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1
Simplify $\sin\left(x\right)\cos\left(x\right)$ using the trigonometric identity: $\sin(2x)=2\sin(x)\cos(x)$
$f\left(x\right)=\frac{\sin\left(2x\right)}{2}-x^2$
Final answer to the problem
$f\left(x\right)=\frac{\sin\left(2x\right)}{2}-x^2$
