Math Problem Statement
a) Graph the function f(x)equals x squared plus 6 x . b) Draw the tangent lines to the graph at the points whose x-coordinates are negative 5 , negative 4 , and negative 2 . c) Find f prime left parenthesis x right parenthesis by determining ModifyingBelow lim With h right arrow 0 StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFraction . d) Find f prime left parenthesis negative 5 right parenthesis , f prime left parenthesis negative 4 right parenthesis , and f prime left parenthesis negative 2 right parenthesis . These slopes should match those of the lines in part (b).
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Quadratic Functions
Tangent Lines
Formulas
Quadratic function: f(x) = ax^2 + bx + c
Derivative definition: f'(x) = lim(h -> 0) [(f(x + h) - f(x)) / h]
Derivative of a quadratic function: f'(x) = 2x + b
Theorems
Limit definition of the derivative
Slope of tangent line equals the derivative at a point
Suitable Grade Level
Grades 11-12
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