Calculus : Maxima and Minima

Question

Tim is working with the function g(x) = sqrt(175-x^2)

a. Tony graphs g(x), and says that the domain (-oo, oo). Explain why that is not true.

b. Tony also believes that, “the lines of the graph are straight.” Explain how you know this isn’t true, and describe how you can determine the curvature of the parts of the graph (either concave up or down).

Answer 1

Domain: the argument of the square root must be non-negative, so 175 - x² ≥ 0 is required.

 

That is, 175 ≥ x² or |x| ≤ 5√35.  

 

Domain: [-5√35, 5√35].

 

The lines of the graph are not straight because this is not the equation of a line! The concavity is determined by the behavior of y" (as usual).