Compute the average rate of change of the given function over the interval [x,x+

ID: 2003099 • Letter: C

Question

Compute the average rate of change of the given function over the interval [x,x+h]. Here we assume [x,x+h] is in the domain of the function.

f(x)=5x^2+6x-4

The height of an object off the ground, h (in feet) t seconds after it is launched into the air is given by

h(t)=-16t^2+96t, (t is in between 0 and 6)

Find the average rate of change of h over the interval [3,6]

Interpret you result.

During the last 3 seconds of the object's time in the air, it is _______ at an average rate of ______ feet per second.

average rate of change of function = [ f(x+h) - f(x) / (x+h - x) ]

average rate of change of function = 5(x+h)^2 + 6(x+h) - 4 - ( 5x^2 + 6x - 4) / h

average rate of change of function = 5x^2 + 5h^2 +10xh +6x+6h - 4 -5x^2-6x + 4 / h

average rate of change of function = (5h^2 +6h + 10xh) /h

average rate of change of function = 5h + 10x + 6

b) average rate of change of h = [f(6) - f(3)] / (6-3)

average rate of change of h = [ -16*6^2 + 96*6 - (-16*3^2 +96*3) ] / 3

average rate of change of h = -48

during the last three seconds the object is moving in opposite direction at an average rate of 48 ft/s

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