Final answer:
To find the expression for (f(1 + h)-f(1))/h for f(x) = 7x² - 2x + 9, we compute f(1 + h) and f(1), subtract, divide by h, and simplify to achieve the form ah + b, eliminating terms and checking for reasonableness along the way.
Step-by-step explanation:
To simplify the quotient (f(1 + h)-f(1))/h for the function f(x) = 7x² - 2x + 9, we will first need to calculate f(1 + h) and f(1). Once we have those, we can substitute them back into the original quotient expression.
- Calculate f(1 + h): f(1 + h) = 7(1 + h)² - 2(1 + h) + 9.
- Expand and simplify the expression for f(1 + h).
- Calculate f(1): f(1) = 7(1)² - 2(1) + 9 = 14.
- Subtract f(1) from f(1 + h).
- Divide the result by h and simplify to get it into the form ah + b.
Once we have followed these steps, we will obtain a simplified expression for the original quotient, which will be the answer to the question. Remember to eliminate terms wherever possible to simplify the algebra and check the answer to ensure it is reasonable.