Compare the properties of the functions D(x)=5x-4/3x^-2x+1 C(x)=2x-1/3x^+4x-5

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embizze eNotes educator| Certified Educator

`D(x)=5x-4/3 x^(-2x+1) ` and `C(x)=2x-1/3x^(4x-5) ` :

D(x) has a domain ` x>=0` and range `y>=0 ` . The y-intercept and the only x-intercept are at (0,0). The function is increasing on its domain and thus has no maximum. It has a minimum at x=0.

C(x) has a domain x>0, and the range is approximately y<2.55953. There is no y-intercept, and the two x-intercepts are at approximately x=0.6059 and x=2.1027. The function has a maximum at approximately (1.62748,2.55953) with no minimum. The graph is concave down everywhere on the domain