Final answer:
To find the derivative using the limit definition for the function y = 2x² - 5x + 1, substitute the function into the difference quotient and simplify. Then, take the limit as h approaches 0.
Step-by-step explanation:
To use the limit definition to find the derivative of the function y = 2x² - 5x + 1, you need to find the limit of the difference quotient as h approaches 0. The difference quotient is given by:
(f(x + h) - f(x)) / h
Substituting the function into the difference quotient and simplifying, you get:
(2(x + h)² - 5(x + h) + 1 - (2x² - 5x + 1)) / h
Expand and simplify the expression, and then take the limit as h approaches 0 to find the derivative.