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.

Algebra ->  Linear-equations -> 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.       Log On


   

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) About Me  (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 x=-4 to x=0 is:
%28f%280%29-f%28-4%29%29%2F%280-%28-4%29%29++
=%28f%280%29-f%28-4%29%29%2F%280%2B4%29
=%28f%280%29-f%28-4%29%29%2F4

now find f%28x%29+=2x%5E3+when x=0
f%280%29=2%2A0%5E3=0
find f%28x%29+=2x%5E3 when x=-4
f%28-4%29=2%2A%28-4%29%5E3=2%28-64%29=-128
plug it in %28f%280%29-f%28-4%29%29%2F4
=%280-%28-128%29%29%2F4
=128%2F4
=32=> rate of change of f%28x%29+=2x%5E3 from -4 to+0


Answer by rothauserc(4718) About Me  (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
: