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Question

At what point of the curve y=x2 does the tangent make an angle of 45o with the x-axis?

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Solution

The required point be (x,y)
The tangent makes an angle of 45o with the xaxis.
Slop of the tangent =tan45o=1
Since, the point lies on the curve.
Now, y=x2
Differentiate w.r.t x,
dydx=2x
Slop of the tangent =(dydx)(x,y)=2x
2x=1 [ Given ]
x=12
Now,
y=x2=(12)2=14
(x,y)=(12,14)



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