What is the average rate of change for the function f x 7x3

What is the average rate of change for the function f (x) = 7x^3 - 2x^2 for the values x = 1 and x = 4? b. What is the instantaneous rate of change for the function f (x) = 7x^3 - 2x^2 at x = 2? f\' (x)= f\' (2)=

Solution

Q7. (a) f(x) = 7x³ -2x²   for values x = 1 and x = 4

Average rate of change = [f(4) - f(1)]/[4-1] =[ 7(4)³-2(4)² - (7(1)³-2(1)²)]/3

= (416 - 5)/3 = 411/3 = 137

Therefore, Average rate of change = 137

(b) Instantaneous rate of change given by :   f\'(x) = 21x² - 4x

f\'(2) = 21(2)² - 4(2) = 84 - 8 = 76

Therefore, f\'(2) = 76