SOLUTION: Find the average rate of change of f(x) =2x^3 from -4 to 0 Need this solved step by step line by line with explanation per line. Thank you.

Question 1139374: Find the average rate of change of f(x) =2x^3 from -4 to 0
Need this solved step by step line by line with explanation per line.
Thank you.
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Average rate of change is just the slope between the 2 points.

so, average rate of change on to is:

=
=

now find when

find when

plug it in
=
=
==> rate of change of from to

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
slope = average rate of change = (f(b) - f(a)) / (b - a), where b is the upper bound of the interval and a is the lower bound of the interval
:
a = -4, b = 0
:
f(0) = 2 * 0^3 = 0
:
f(-4) = 2 * (-4)^3 = -128
:
average rate of change = (0 - (-128)) / (0 - (-4)) = 32
:
the equation of the secant line through the two points (-4,-128) and (0,0)
:
y = mx +b
:
y = 32x +b
:
pick one of the points
:
0 = 32(0) + b
:
b = 0
:
y = 32x is the equation of the secant line
:
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