Question 949345
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.