Question

7. The curve y = x + 2x2 – 3x has a gradient of 4 at points A and B.
Find the x-coordinates of A and B.​

Answer 1

Answer:

Let the point is P(a,b)

Now the given curve is y=x

2

+3x+4

Differentiating w.r.t x

dx

dy

=2x+3

Thus slope of tangent at P is =(

dx

dy

)

(a,b)

=2a+3

Hence equation of tangent at P is given by, (y−b)=(2a+3)(x−a)

But given that tangent passes through origin

⇒(0−b)=(2a+3)(0−a)⇒2a

2

+3a=b..(1)

Also the point P lies on the given curve,

b=a

2

+3a+4...(2)

Solving (1) and (2) we get the required point P coordinate

which are (−2,2)or(2,14)

Hence, option 'A' is correct.

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