# How do you find the points where the graph of the function #f(x) = x^4-4x+5# has horizontal tangents and what is the equation?

##### 1 Answer

Feb 28, 2016

at

#### Explanation:

A horizontal tangent occurs whenever the function's derivative equals

To find the function's derivative, use the **power rule**.

#f(x)=x^4-4x+5#

#f'(x)=4x^3-4#

Find the points when

#4x^3-4=0#

#4x^3=4#

#x^3=1#

#x=1#

There is a horizontal tangent at

We can check a graph of

graph{(x^4-4x+5-y)(y-0x-2)=0 [-19.92, 20.63, -3.52, 16.74]}