// Numbas version: exam_results_page_options {"name": "Intersection of graphs - graphically", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Intersection of graphs - graphically", "tags": [], "metadata": {"description": "Find intersection of two graphs using GDC.", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Let $f(x) = xe^{-x}$ and $g(x) = -3f(x) +1$.

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The graphs of $f$ and $g$ intersect at $x=p$ and $x=q$ where $p<q$.

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", "advice": "

This problem should be solved by sketching the graphs on your graphics calculator and using the intersect option to find where they cross. 

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The two values are

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$p =$ {p} and

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$q =$ {q}

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but note that answers should be given o 3 significant figures

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$p = 0.357$ and 

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$q = 2.15$

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you may have been penalised if you rounded incorrectly.

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Intersection 1.

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Intersection 2

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Write down the value of $p$.

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Write down the value of $q$.

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