Find the average rate of change of the function on the interval specified for real number b. f(x) = 6x2 − 7 on [1, b]

Answer 1

f(x) = 6x^2 - 7 on the interval [1,b]

average rate of change = (f(b)-f(1))/(b-1)

= (6b^2 -7 - (6-7))/(b-1)

= (6b^2 -6)/(b-1)

= 6(b^2-1)/(b-1)

= 6(b+1)

= 6b+6

as b approaches 1, slope = 6(1)+6 = 12 = f'(x)= the derivative at x= 1