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

Slide33.JPG

Slide34.JPG
Slide35.JPG

  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 14 (OR 2nd Question) For the curve y = 5x โˆ’ 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 โˆ’ 2x3 ๐‘‘๐‘ฅ/๐‘‘๐‘ก = 2 units/sec We need to find how fast the slope is changing We know that Slope = ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = (๐‘‘(5๐‘ฅ โˆ’ 2๐‘ฅ^3))/๐‘‘๐‘ฅ = 5 โ€“ 6x2 How was slope is changing is (๐‘‘(๐‘†๐‘™๐‘œ๐‘๐‘’))/๐‘‘๐‘ก Finding it (๐‘‘(๐‘†๐‘™๐‘œ๐‘๐‘’))/๐‘‘๐‘ก = (๐‘‘(5 โˆ’ 6๐‘ฅ^2))/๐‘‘๐‘ก = 0 โ€“ 12x ๐‘‘๐‘ฅ/๐‘‘๐‘ก = โ€“12x ๐‘‘๐‘ฅ/๐‘‘๐‘ก Putting x = 3 and ๐‘‘๐‘ฅ/๐‘‘๐‘ก = 2 units/sec = โ€“12 ร— 3 ร— 2 = โ€“72 So, Slope is decreasing at the rate of 72 units/sec

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.