Determine the value of:

a) g(-4)

b) g(-2)

c) g(1)

d) g(4)

The absolute maximum of g(x) occurs when x=....?

The absolute maximum of g(x) is...?

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- Jan 18th 2009, 05:52 PMMy Little PonyIntegration of a piece wise function?
Determine the value of:

a) g(-4)

b) g(-2)

c) g(1)

d) g(4)

The absolute maximum of g(x) occurs when x=....?

The absolute maximum of g(x) is...? - Jan 18th 2009, 06:12 PMo_O
Drawing $\displaystyle f(x)$ out would help. You will see that your graph basically consists of line segments.

Recall that an integral represents the net area under the curve (from the curve to the x-axis). So all you're doing is calculating the areas of the rectangles (taking into account of the signs).

For example, to find $\displaystyle g(1) = \int_{-3}^{1} f(t) \ dt$, we want to find the area under the curve from $\displaystyle x = -3$ to $\displaystyle x = 1$

Since it's a piecewise function, we're going to have to break the integral up into two: $\displaystyle g(1) = \int_{-3}^{1} f(t) \ dt = \int_{-3}^{0} f(t) \ dt + \int_0^1 f(t) \ dt$

If you look at your graph, the two integrals corresponds to the area under each rectangle that is created. I assume you know how to find the area of a rectangle so hopefully you'll be good from here.