Question 14 (OR 2nd Question) For the curve y = 5x β 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 β 2x3
ππ₯/ππ‘ = 2 units/sec
We need to find how fast the slope is changing
We know that
Slope = ππ¦/ππ₯
= (π(5π₯ β 2π₯^3))/ππ₯
= 5 β 6x2
How was slope is changing is
(π(πππππ))/ππ‘
Finding it
(π(πππππ))/ππ‘ = (π(5 β 6π₯^2))/ππ‘
= 0 β 12x ππ₯/ππ‘
= β12x ππ₯/ππ‘
Putting x = 3 and ππ₯/ππ‘ = 2 units/sec
= β12 Γ 3 Γ 2
= β72
So, Slope is decreasing at the rate of 72 units/sec

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Davneet Singh

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.