Consider the quadratic function g(x)=x²-4x+36. Define a new function S(x) by S(x)=the slope of the diagonal line through g(x) = 21. (a) Find the positive critical value of S(x). (b) Determine whether S(x) is concave up or concave down at the critical value you found in (a) and use the Second Derivative Test to determine if the critical value gives a local maximum or a local minimum. S(x) is ---Select-- A at the critical value. Therefore, the critical value gives a -Select-- e of S(x). (c) If x must be positive, what is the lowest possible value of S(x) ?

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