Final answer:
To find f(a), we replace x with a in the function f(x) = 2x⁷. To find f(ah), we replace x with ah in the function f(x) = 2x⁷. The difference quotient for the function f(x) = 2x⁷ is (2(x + h)⁷ - 2x⁷) / h.
Step-by-step explanation:
To find f(a), we replace x with a in the function f(x) = 2x⁷. So, f(a) = 2a⁷.
To find f(ah), we replace x with ah in the function f(x) = 2x⁷. So, f(ah) = 2(ah)⁷.
The difference quotient for a function is given by the formula: (f(x + h) - f(x)) / h. In this case, the function is f(x) = 2x⁷. So, the difference quotient for this function is (2(x + h)⁷ - 2x⁷) / h. This expression captures the function's incremental change between x and x+h relative to h, crucial in understanding the function's instantaneous rate of change at a given point.