Graph of $ g $
3. The graph of the continuous function $ g $, the derivative of the function $ f $, is shown above. The function $ g $ is piecewise linear for $ -5 \leq x

Question

Graph of $ g $
3. The graph of the continuous function $ g $, the derivative of the function $ f $, is shown above. The function $ g $ is piecewise linear for $ -5 \leq x<3 $, and $ g(x)=2(x-4)^{2} $ for $ 3 \leq x \leq 6 $.
(a) If $ f(1)=3 $, what is the value of $ f(-5) $ ?
(b) Evaluate $ \int_{1}^{6} g(x) d x $.
(c) For $ -5<x<6 $, on what open intervals, if any, is the graph of $ f $ both increasing and concave up? Give a reason for your answer.
(d) Find the $ x $-coordinate of each point of inflection of the graph of $ f $. Give a reason for your answer.

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