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The angle between the tangent lines to t...

The angle between the tangent lines to the graph of the function `f(x) = int_2^x (2t-5)dt` at the points where the graph cuts the x-axis is

A

`(pi)/6`

B

`(pi)/4`

C

`(pi)/3`

D

`(pi)/2`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x) = int_(2)^(x) (2t-5)dt`
`=(t^(2)-5t)_(2)^(x)`
`=(x^(2)-5x)-(4-10)`
`=x^(2) -5x +6`
`(x-2)(x-3) = 0, x= 2,3`
`f'(x) = 2x-5`
`(f'(x))_(x=2) = -1, (f'(x))_(x=3) = 1`
Hence angle = `(pi)/2`.
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