Math Problem Statement

Find the indicated quantities for 𝑓(𝑥) = 3𝑥 2 (A) The slope of the secant line through the points (2, f (2)) and (5, f (5)) on the graph of y = f (x). (B) The slope of the secant line through the points (2, f (2)) and (2 + h, f (2 + h)), h ≠ 0. Simplify your answer. (C) The slope of the graph at (2, f (2)).

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Calculus
Derivatives
Secant Lines

Formulas

Slope of secant line: m = (f(x2) - f(x1)) / (x2 - x1)
Slope of secant line with h: m = (f(2 + h) - f(2)) / h
Derivative of a function: f'(x) = d/dx (f(x))

Theorems

Derivative definition
Slope of secant line as a limit of tangent

Suitable Grade Level

Grades 11-12 or Calculus I