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]}