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For the curveΒ  y = 5x βˆ’ 2x 3 , if x increases at the rate of 2 units/sec, then at x = 3 the slope of the curve is changing at _________

For curveΒ  y = 5x βˆ’ 2x^3, if x increases at rate of 2 units/sec, then

Question 14 (OR 2nd Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 2
Question 14 (OR 2nd Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 3

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Question 14 (OR 2nd Question) For the curve y = 5x βˆ’ 2x3, if x increases at the rate of 2 units/sec, then at x = 3 the slope of the curve is changing at _________ Given y = 5x βˆ’ 2x3 𝑑π‘₯/𝑑𝑑 = 2 units/sec We need to find how fast the slope is changing We know that Slope = 𝑑𝑦/𝑑π‘₯ = (𝑑(5π‘₯ βˆ’ 2π‘₯^3))/𝑑π‘₯ = 5 – 6x2 How was slope is changing is (𝑑(π‘†π‘™π‘œπ‘π‘’))/𝑑𝑑 Finding it (𝑑(π‘†π‘™π‘œπ‘π‘’))/𝑑𝑑 = (𝑑(5 βˆ’ 6π‘₯^2))/𝑑𝑑 = 0 – 12x 𝑑π‘₯/𝑑𝑑 = –12x 𝑑π‘₯/𝑑𝑑 Putting x = 3 and 𝑑π‘₯/𝑑𝑑 = 2 units/sec = –12 Γ— 3 Γ— 2 = –72 So, Slope is decreasing at the rate of 72 units/sec

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.