Math Problem Statement
For each part, use the first derivative test to find the intervals of increase or decrease and any local extrema of the function. (6 marks) π(π₯) =3π₯2βπ₯β2/x-2 β‘β‘β‘πβ²(π₯) =3π₯2β12π₯+4/(π₯β2)2 b) π(π₯) = π₯ ln(π₯3) β‘β‘β‘β‘πβ(π₯) = 3 ln(π₯) +3
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
First Derivative Test
Intervals of Increase/Decrease
Critical Points
Rational Functions
Logarithmic Functions
Formulas
First Derivative: f'(x)
Quadratic Formula: x = (-b Β± β(b^2 - 4ac)) / 2a
Derivative of Logarithmic Functions: d/dx [ln(x)] = 1/x
Theorems
First Derivative Test
Quadratic Equation Theorem
Properties of Logarithms
Suitable Grade Level
Undergraduate Calculus (Calculus I or II)
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