test","extracted_subject":"MATH","extracted_chapter":"DIFFRENTIATION AND APPLICATIONS OF DERIVATIVES","extracted_topic":"DIFFERENTIATION OF IMPLICIT FUNCTION, PARAMETRIC AND COMPOSITE FUNCTIONS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1629.png?top_left_x=532&top_left_y=678&width=532&height=215&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e6f425d76b7ab31c39e","slug":"if-m-is-the-slope-of-a-tangent-to-the-curve-esupys","content":"If m is the slope of a tangent to the curve e^y = 1 + x², then","options":[{"_id":"68aab54a7f15af4716dbdad7","text":"\\|m\\| \\> 1","sequence":0,"isCorrect":false},{"_id":"68aab54a7f15af4716dbdad8","text":"m \\< 1","sequence":1,"isCorrect":false},{"_id":"68aab54a7f15af4716dbdad9","text":"\\|m\\| \\< 1","sequence":2,"isCorrect":false},{"_id":"68aab54a7f15af4716dbdada","text":"\\|m\\| ≤ 1","sequence":3,"isCorrect":true}],"correct_answer":"\\|m\\| ≤ 1","explanation":"e^y\\(\\frac{dy}{dx}\\) = 2x ⇒ m = \\(\\frac{dy}{dx} = \\frac{2x}{1 + x^{2}}\\) (Q e^y = 1 + x²)\n\n\\| m \\|= \\(\\frac{2|x|}{1 + x^{2}}\\) Q1+ \\| x \\|² – 2\\| x \\| = (1– (\\| x \\|))² ≥ 0\n\n⇒ 1 + \\| x \\|² ≥ 2\\| x \\| ∴ \\|m\\| ≤ 1","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:35.461Z","__v":0,"vector_store_id":"2ce94961-f6f8-4a09-97c3-cf7a8d6479c4","updated_at":"2024-08-30T21:49:35.461Z","isStarred":false},"params":{"questionSlug":"if-m-is-the-slope-of-a-tangent-to-the-curve-esupys"}}]}]]

Question: If m is the slope of a tangent to the curve e<sup>y</sup> = 1 + x<sup>2</sup>, then...

Solution