Final answer:
To calculate the difference quotient for the function f(x) = 5x³, you need to use the formula (f(x+h) - f(x)) / h. Plug in the values and simplify the expression to obtain the difference quotient.
Step-by-step explanation:
To calculate the difference quotient for the function f(x) = 5x³, we need to use the formula:
dQ = (f(x+h) - f(x)) / h
Let's plug in the values:
f(x) = 5x³
f(x+h) = 5(x+h)³ = 5(x³ + 3x²h + 3xh² + h³)
dQ = (5(x³ + 3x²h + 3xh² + h³) - 5x³) / h
dQ = (5x³ + 15x²h + 15xh² + 5h³ - 5x³) / h
dQ = (15x²h + 15xh² + 5h³) / h
dQ = 15x² + 15xh + 5h²