Question 14 (OR 2nd Question) For the curve y = 5x โ 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 โ 2x3
๐๐ฅ/๐๐ก = 2 units/sec
We need to find how fast the slope is changing
We know that
Slope = ๐๐ฆ/๐๐ฅ
= (๐(5๐ฅ โ 2๐ฅ^3))/๐๐ฅ
= 5 โ 6x2
How was slope is changing is
(๐(๐๐๐๐๐))/๐๐ก
Finding it
(๐(๐๐๐๐๐))/๐๐ก = (๐(5 โ 6๐ฅ^2))/๐๐ก
= 0 โ 12x ๐๐ฅ/๐๐ก
= โ12x ๐๐ฅ/๐๐ก
Putting x = 3 and ๐๐ฅ/๐๐ก = 2 units/sec
= โ12 ร 3 ร 2
= โ72
So, Slope is decreasing at the rate of 72 units/sec

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.