How many tangents are parallel to x-axis for the curve y = x² - 4x + 3?

Question

Question

Answer 1

Concept:

The slope of the tangent to the given curve y = f(x) at the point p is given by f’(x).

Calculation:

Given curve: y = x² - 4x + 3

Differentiating with respect to x, we get

\(\rm \frac{dy}{dx} = 2x - 4\)

Given: Tangents are parallel to the x-axis

Therefore, \(\rm \frac{dy}{dx} = 0\)

⇒ 2x - 4 = 0

∴ x = 2

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

Hence, only 1 tangent exists.