find the equation of the tangent line to the graph of (f(x) = x^2 - 19) at the point ((5, 6)).

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Tangent Line Equation", "Power Rule Differentiation" ], "current_concepts": [ "Derivative Definition", "Tangent Line Equation", "Power Rule Differentiation" ] } ## Find the derivative of the function $$ f'(x) = \frac{d}{dx}(x^2 - 19) = 2x $$ ## Calculate the slope at the given point $$ m = f'(5) = 2(5) = 10 $$ ## Write the equation of the tangent line $$ \begin{aligned} y - y_1 &= m(x - x_1) \ y - 6 &= 10(x - 5) \ y - 6 &= 10x - 50 \ y &= 10x - 44 \end{aligned} $$ $y = 10x - 44$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Calculus", "Tangent Line Equation" ] }

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Question

Explanation:

Find the derivative of the function

Calculate the slope at the given point

Write the equation of the tangent line

Answer: