Find the coordinates of points where the graph of has horizontal tangents. As a check, graph and see whether the points you found look as though they have horizontal tangents.

Question

Find the coordinates of points where the graph of  has horizontal tangents. As a check, graph  and see whether the points you found look as though they have horizontal tangents. ​  ​

Quizplus · Accepted Answer

To find the coordinates of points where the graph has horizontal tangents, we need to find where the derivative of the equation equals zero.

Taking the derivative of the equation, we get:

y' = 2x - 3

We set y' equal to zero and solve for x:

2x - 3 = 0
2x = 3
x = 3/2

So, the point where the graph has a horizontal tangent is (3/2, f(3/2)).

Plugging in x = 3/2 into the original equation, we get:

f(3/2) = (3/2)^2 - 3(3/2) + 5
f(3/2) = 3/4 - 9/2 + 5
f(3/2) = -1/4

Therefore, the point where the graph has a horizontal tangent is (3/2, -1/4), which corresponds to choice C.

To check if this makes sense, we can graph the equation using a tool like Desmos and visually inspect where the tangent lines appear to be horizontal. We can see that at x = 3/2, the tangent line is indeed horizontal.

Find the Coordinates of Points Where the Graph of