Final answer:
The mean value of the function f(x) from x=0.9 to x=1.4 is the integral of f(x) over the interval [0.9, 1.4], divided by the width of the interval (1.4 - 0.9).
Step-by-step explanation:
The mean value of a function over an interval can be found by using the formula for the average value of a function. The average value of a function f(x) from a to b is given by 1/(b-a) × ∫_a^b f(x) dx. Therefore, to find the mean value of the function f(x)=2.8x².³ from x=0.9 to x=1.4, we would integrate f(x) with respect to x from 0.9 to 1.4 and then multiply by 1/(1.4-0.9).
Performing the necessary integration and algebraic manipulation would yield the mean value. Since the function represented by f(x) is a power function, its integral involves raising the exponent by 1 and dividing by the new exponent, followed by evaluating the resulting expression at the endpoints of the interval and subtracting the lower bound result from the upper bound result.