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Find the average rate of change of g(x)= -4x^3+1 from x= -4 to x = 1

1 Answer

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Answer:


Rate = -52

Explanation:

Given


g(x) = -4x^3 + 1

x = -4 to x = 1

Required

Determine the average rate of change

This is calculated using:


Rate = (g(b) - g(a))/(b - a)

Where


a = x = -4


b = x = 1

Calculating g(b):

g(b) = g(1)

If
g(x) = -4x^3 + 1, then


g(1) = -4(1)^3 + 1


g(1) = -4*1 + 1


g(1) = -4 + 1


g(1) = -3

Calculating g(a):

g(a) = g(-4)

If
g(x) = -4x^3 + 1, then


g(-4) = -4(-4)^3 + 1


g(-4) = -4*-64 + 1


g(-4) = 256 + 1


g(-4) = 257

So, the formula:


Rate = (g(b) - g(a))/(b - a)

becomes


Rate = (g(1) - g(-4))/(1 - (-4))


Rate = (g(1) - g(-4))/(1+4)


Rate = (g(1) - g(-4))/(5)


Rate = (-3 - 257)/(5)


Rate = (-260)/(5)


Rate = -52

User Charit
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