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For the curve y=4x^3-2x^5, find all the ...

For the curve `y=4x^3-2x^5,` find all the points at which the tangents pass through the origin.

A

`(-2,14)`

B

`(2,14)`

C

`(2,-2)`

D

`(-2,2)`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`(dy)/(dx)` at `x_(1),y_(1)` must equal to `(y_(1)-0)/(x_(1)-0)`
Therefore `2x_(1)+3=(x_(1)^(2)+3x_(1)+4-0)/(x_(1)-0)`
Hence `x_(1)^(2)=4impliesx_(1)=+-2impliesy_(1)=14,2`
`(2,14),(-2,2)`s
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