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Evaluate the difference quotient for the given function. Simplify your answer.
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Text solutionVerified
Key Concepts: Difference Quotient, Simplification Of Expressions
Explanation:
To evaluate the difference quotient, we substitute the function f(x) in the definition of difference quotient. The expression f(3+h) means substitute x in f(x) with 3+h, and f(3) means substituting x in f(x) with 3.
Step by Step Solution:
Step 1. Substitute x with (3+h) in the given function f(x) to get f(3+h) = 4 + 3(3+h)-(3+h)^2.
Step 2. Simplify the expression: f(3+h) = 4 + 9 + 3h - h^2 - 6h - 9 = -h^2 -3h + 4.
Step 3. Substitute x with 3 in the given function f(x) to get f(3) = 4 + 3(3)-3^2 = -5.
Step 4. Substitute the simplified expressions f(3+h) = -h^2 -3h + 4 and f(3) = -5 in the difference quotient to get:
Step 5. difference quotient = [f(3+h) - f(3)]/h = [[-h^2 -3h + 4] - [-5]]/h = (-h^2 -3h + 9)/h
Final Answer:
(-h^2 -3h + 9)/h
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Question Text | Evaluate the difference quotient for the given function. Simplify your answer. |
Topic | All Topics |
Subject | AP Calculus BC |
Class | Class 11 |
Answer Type | Text solution:1 |