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f is a continuous function with a domain [−3, 9] such that

f of x equals 3 for x between negative 3 and 0 including negative 3, equals negative 1 times x plus 3 for x between 0 and 6 inclusive, and equals negative 3 for x greater than 6 and less than or equal to 9
and let g of x equals the integral from negative 2 to x of f of t, dt.

On what interval is g increasing? Justify your answer.

For 0 ≤ x ≤ 6, express g(x) in terms of x. Do not include +C in your final answer.

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1 answer

  1. why all those messy words? You appear to be saying

    f(x) =
    3 for -3 <= x < 0
    -x+3 for 0 <= x <= 6
    -3 for 6 < x <= 9

    g is increasing where f is positive: [-2,0)U(3,6]

    g(x) = ∫[-2,0] 3 dt + ∫[0,x] -t+3 dt
    = 6 + (-x^2/2 + 3x)+3 for 0<=t<=6

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