Concept:Increasing and Decreasing Functions DefinitionIncreasing Function: A function f(x) is said to be increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ? f(y).Decreasing Function: A function f(x) is said to be decreasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ? f(y).Strictly Increasing Function: A function f(x) is said to be strictly increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) < f(y).Strictly Decreasing Function: A function f(x) is said to be strictly decreasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) > f(y).Calculation:\(\displaystyle f(x) = \frac{x^3}{3}-\frac{7x^2}{2} + 6x + 5\)? \(\displaystyle f'(x)=x^2-7x+6\)For the function to decreasing, f'(x) < 0? \(\displaystyle f'(x)=x^2-7x+6\)? f'(x) = x2 - 6x - x + 6? f'(x) = x(x - 6) - 1(x - 6)? f'(x) = (x - 1) (x - 6)From the graph, f'(x) is negative in the interval (1,6).? The function is decreasing in (1, 6).