Math Problem Statement

Find the points on the graph of the function that are closest to the given point.

f(x) = x2,

    

(0, 9)

smaller x-value

(xy)

=        larger x-value

(xy)

=       

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Optimization
Parabolas
Distance Minimization

Formulas

Distance formula: d = √((x - x₁)^2 + (y - y₁)^2)
Equation of a parabola: y = f(x) = x²
Derivative of distance function

Theorems

Critical points from derivatives (setting the first derivative to zero)
Optimization via minimizing the square of the distance

Suitable Grade Level

Grades 11-12 (Pre-Calculus/Calculus)