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The derivative of the function represent...

The derivative of the function represented parametrically as `x=2t=|t|,y=t^3+t^2|t|a tt=0` is a. -1 b. 1 c. 0 d. does not exist

A

`-1`

B

0

C

1

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`x=2t-|t|, y=t^(3)+t^(2)|t|`
`rArr" "x=3t, y=0` when t lt 0
X = t, `y=2t^(3)` when `x ge 0`
Eliminating the parameter t, we get
`y={{:(0",",xlt0),(2x^(3)",",xge0):}` ltbr. Differentiating w.r.t. x, we get
`(dy)/(dx)={{:(0",",xlt0),(6x^(2)",",xge0):}`
Hence, the function is differentiable every where and its derivative at x = 0 (t = 0) is 0.
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