CBSE Class 12 Sample Paper for 2020 Boards

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

## For the curveย  y = 5x โ 2x 3 , if x increases at the rate of 2 units/sec, then at x = 3 the slope of the curve is changing at _________

Get live Maths 1-on-1 Classs - Class 6 to 12

### Transcript

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 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 โ 2๐ฅ^3))/๐๐ฅ = 5 โ 6x2 How was slope is changing is (๐(๐๐๐๐๐))/๐๐ก Finding it (๐(๐๐๐๐๐))/๐๐ก = (๐(5 โ 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