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For questions 1, 2, and 3, consider the function \(f(x) = x^3-5x^2+7x\)

1.  On what interval(s) is the function \(f\) decreasing?

a.  \( (-\infty, 0)\)

b.  \( (1, \frac{7}{3})\)

c.  \( (1, 2)\)

d.  \( (1, \frac{5}{2})\)

e.  \( (\frac{5}{3}, \infty)\)

2.  On what interval(s) is the graph of the function \(f\) concave up?

a.  \( (0,\infty)\)

b.  \( (-\infty, 1), (\frac{7}{3}, \infty)\)

c.  \( (-\infty, 1), (2, \infty)\)

d.  \( (1, \frac{5}{2})\)

e.  \( (\frac{5}{3}, \infty)\)

3.  How many relative maxima does the function \(f\) have?

a.  None

b.  One

c.  Two

d.  Two and a half

e.  Three

4.  How many points of inflection does the function \(g(x) = x^4\) have?

a.  None

b.  One

c.  Two

d.  Two and a half

e.  Three