SOLUTION: 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)

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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