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If the normal to the curve `y=f(x)` at the point `(3,4)` makes an angle `(3pi)/4` with the positive x-axis, then `f'(3)=` (a) `-1` (b) `-3/4` (c) `4/3` (d) `1`

A

`-1`

B

`-(3)/(4)`

C

`(4)/(3)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
Slope of the normal to the curve at an angle `theta=(3pi)/(4)` is tan`(3pi)/(4)=-1`
But slope of normal=`(-1)/(dy//dx)`
`therefore((dy)/(dx))_((3,4))=1impliesf'(3)=1`
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