Question

For the curve y = 5x – 2x^3, if x increases at the rate of 2units/sec
then at x= 3 the slope of the curve is changing at____
​

Answer 1

Let m be the slope of the curve at an arbitrary point (x,y) on it. Then,

m=

dx

dy

m=

dx

d(5x−2x

3

)

m=5−6x

2

Given,

dt

dx

=2 units/sec.

Now, m=5−6x

2

dt

dm

=−12x

dt

dx

(

dt

dm

)

x=3

=−12×3×2=−72 units/sec

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