Question

How do you find the points where the graph of the function `y = x^2 + 1` has horizontal tangents and what is the equation?

Answer 1

y = 1

Explanation:

horizontal tangents are tangents which are parallel to the x-axis. These are found by differentiating the function and equating to zero.

horizontal tangents occur at stationary points.

`f(x) = x^2 + 1`

`rArr f'(x) = 2x`

to find stationary points let 2x = 0 → x = 0

x = 0 : y = 0 + 1 =1 hence , stationary point at (0 , 1 )

hence equation of horizontal tangent is y = 1
graph{x^2 +1 [-10, 10, -5, 5]}