Question

How many tangents are parallel to x-axis for the curve $y=x^2-4x+3$ ?

• A. 1
• B. 2
• C. 3
• D. No tangent is parallel to x-axis.

Answer 1

Answer: (A)

1

Slope of the tangent is $\frac{dy}{dx}$

So, $\frac{dy}{dx}=2x-4$

Tangent parallel to x-axis. So, slope of tangent should be $0.$

$\Rightarrow 2x-4=0$

$\Rightarrow x=2$ is the only point where slope is parallel to x-axis.

So, only 1 tangent exists.