BPSC 48th to 52nd Exam Prelims 2008 Solved Paper

Question : 32 of 150

Marks: +1, -0

The point on the curve y

= 1 + 2x – 3x^2

at which the tangent makes an angle of 45° with the x-axis is

Solution:

Explanation: From the question Curve

y=1+2 x-3 x^{2}

\;{d y}/{d x}=2-6 x

\;{d y}/{d x}=\tan 45^{∘}

2-6 x=1 ⇒ x=\;{1}/{6}

∴ y=1+\;{2}/{6}-\;{3}/{36}

⇒ y=\;{12+4-1}/{12}=\;{15}/{12}=\;{5}/{4}

∴

The point

=(\;{1}/{6}, \;{5}/{4})

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