Find all values of 
such that 
. Answer with interval notation.
Please enter your response in interval notation. Refer to Formatting Tips below for detailed instructions on formatting your response.
+130511 c^3 + 4c > 5c^2 subtract 5c^2 from both sides
c^3 + 4c - 5c^2 > 0 rearrange
c^3 - 5c^2 + 4c > 0 set this = 0 and factor
c^3 - 5c^2 + 4c = 0
c(c^2 -5c + 4) = 0
c(c-4)(c-1) = 0
And setting each factor to 0 , we have that c =0, c = 4 and c =1
Now, adding back the inequality sign, we have
c(c-4)(c-1) > 0
And if c < 0 , c(c-4)(c-1) < 0
And if c > 0 but < 1 , c(c-4)(c-1) is > 0
And if c > 1 but < 4, c(c-4)(c-1) is < 0
And if c > 4, c(c-4)(c-1) > 0
Here's a graph using 'x" rather than "c".........https://www.desmos.com/calculator/pw1vqn74aq
So, interval notation we have
[0 < c < 1] U [4 < x < ∞]
+130511 c^3 + 4c > 5c^2 subtract 5c^2 from both sides
c^3 + 4c - 5c^2 > 0 rearrange
c^3 - 5c^2 + 4c > 0 set this = 0 and factor
c^3 - 5c^2 + 4c = 0
c(c^2 -5c + 4) = 0
c(c-4)(c-1) = 0
And setting each factor to 0 , we have that c =0, c = 4 and c =1
Now, adding back the inequality sign, we have
c(c-4)(c-1) > 0
And if c < 0 , c(c-4)(c-1) < 0
And if c > 0 but < 1 , c(c-4)(c-1) is > 0
And if c > 1 but < 4, c(c-4)(c-1) is < 0
And if c > 4, c(c-4)(c-1) > 0
Here's a graph using 'x" rather than "c".........https://www.desmos.com/calculator/pw1vqn74aq
So, interval notation we have
[0 < c < 1] U [4 < x < ∞]
