Find the x and y Intercepts f(x)=x^4-4x^3

Problem

ƒ(x)=x4−4*x3

Solution

1. Find the y-intercept by evaluating the function at x=0

ƒ(0)=(0)4−4*(0)3

ƒ(0)=0

2. Set the function to zero to find the x-intercepts.

x4−4*x3=0

3. Factor out the greatest common factor, which is x3

x3*(x−4)=0

4. Apply the zero product property by setting each factor equal to zero.

x3=0⇒x=0

x−4=0⇒x=4

Final Answer

x-intercepts: *(0,0),(4,0); y-intercept: *(0,0)

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