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Question 949345: Someone help me with this please. I highly appreciated.
A function is given. Determine the average rate of change of the function between the given values of the variable.
f(x) = 5x^2; x = 4, x = 4 + h
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! function is given as f(x) = 5x^2
you are asked to find the average rate of change when the value of x goes from x = 4 to x = 4+h
when x = 4, f(4) = 5*4^2 = 5*16 = 80
when x = 4+h, f(4+h) = 5*(4+h)^2 = 5*(4^2+2*4*h+h^2) = 5*(16+8h+h^2) = 80+40h+5h^2
you have:
when x = 4, f(4) = 80
when x = 4+h, f(4+h) = 80+40h+5h^2
the rate of change is equal to f(x+h) - f(x) divided by (x+h)-x which simplifies to:
(f(x+h)-f(x))/h
when x = 4, this becomes (f(4+h)-f(4)/h
since f(4+h) = 80+40h+5h^2 and f(4) = 80, this formula becomes:
(80+40h+h^2-80)/h which becomes:
(40h+h^2)/h which can be further simplified to:
40+h
the average rate of change is equal to 40+h.
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