# How do you find the critical points for #y=x^4-3x^3+5#?

##### 1 Answer

Jan 11, 2017

# (0,5) # and

#(2.25,-3.54) # (2dp)

#### Explanation:

# y = x^4 - 3x^3 + 5 #

Differentiating wrt

# dy/dx = 4x^3 - 9x^2 #

At a critical point,

# => x^2(4x - 9) = 0#

#:. x=0,9/4#

When;

# x=0 => y=5 #

# x=2.25 => y~~-3.54 #

So there are two critical points:

# (0,5) # and#(2.25,-3.54) # (2dp)

We we can see on the graph:

graph{y = x^4 - 3x^3 + 5 [-2, 5, -5.81, 9.99]}