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

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.

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]}

To find the points where the graph of the function y = x^2 + 1 has horizontal tangents, we need to determine the values of x that make the derivative of the function equal to zero.

First, we find the derivative of the function y = x^2 + 1, which is dy/dx = 2x.

Setting dy/dx equal to zero, we have 2x = 0. Solving for x, we find x = 0.

Substituting this value of x back into the original function, we get y = (0)^2 + 1 = 1.

Therefore, the equation of the points where the graph of y = x^2 + 1 has horizontal tangents is (0, 1).