Math Problem Statement
Sketch the graph of the given function. Use technology to approximate the intercepts, coordinates of extrema, and points of inflection to one decimal place. Check your sketch using technology. HINT [See Example 1.] f(x) = 4x3 + 6x2 − 24x + 1
(c) Indicate any points of inflection. (If an answer does not exist, enter DNE.)
(x, y) =
Solution
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Math Problem Analysis
Mathematical Concepts
Cubic Functions
Derivatives
Extrema
Points of Inflection
Formulas
Cubic function: f(x) = ax^3 + bx^2 + cx + d
First derivative: f'(x) = 12x^2 + 12x - 24
Second derivative: f''(x) = 24x + 12
Quadratic equation: ax^2 + bx + c = 0
Theorems
Critical Points Theorem
Inflection Point Theorem
Suitable Grade Level
Grades 10-12
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