For what values of x does the curve y^2x^3-15x^2=4 have horizontal tangent lines

We have the following curve:



To find the tangent lines to the curve we need to use the concept of derivative, but we can’t solve this problem for , thus, let's apply implicit differentiation, so:



Therefore the horizontal lines occurs when , then:



If we substitute this in the original equation we have:



This is an absurd result because it is impossible for a squared number to get a negative number. So the conclusion is that there is no any value of in which the curve has horizontal tangent lines.

sorry i got nothing

step-by-step explanation: