Question

At what point of the curve $y=2x^2-x+1$ tangent is parallel to $y=3x+4$

• A. $(0,1)$
• B. $(1,2)$
• C. $(-1,4)$
• D. $(2,7)$

Answer 1

Answer: (B)

$(1,2)$

Let the point is $P(a,b)$
Now the given curve is $y=2x^2-x+1$
Differentiating w.r.t $x$
$\frac{dy}{dx}=4x-1$
Thus slope of tangent at P is $={\left(\frac{dy}{dx}\right)}_{(a,b)}=4a-1$
But given the tangent is parallel to line $y=3x+4$
$\Rightarrow 4a-1=3\Rightarrow a=1$
Also the point P lies on the given curve,
$b=2a^2-a+1=2$
Therefore, the point P is $(1,2)$
Hence, option 'B' is correct.