Math Problem Statement
The variables x, y, and z are connected by the equation z=y^2 + x^3 + 5x + 9 a) Given that y= 5-x, find the possible values of x for which z has stationary value. b) find the minimum value of z
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Calculus
Stationary Points
Derivatives
Quadratic Equations
Formulas
z = y^2 + x^3 + 5x + 9
y = 5 - x
Derivative formula: dz/dx = 3x^2 + 2x - 5
Quadratic equation: ax^2 + bx + c = 0
Quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a
Theorems
Quadratic Formula
First Derivative Test
Suitable Grade Level
Grades 11-12
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