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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


Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.