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about to only mathematics...

about to only mathematics

A

`-1`

B

`-3//4`

C

`4//3`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
D
Slope of tangent `y = f(x) `is `(dy)/(dx) = f'(x)_("("3, 4")")`
Therefore, slope of normal
`" " = - (1)/(f'(x)_("("3, 4")"))= - (1)/(f'(3))`
But ` " " - (1)/(f' (3)) = tan (( 3pi)/(4))" " ` [ given]
`rArr " " (-1)/(f '(3)) = tan ((pi)/(2) + (pi)/(4)) =-1 `
` therefore " " f' (3) = 1 `
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