Homework #5

# Homework #5 - jiwani(amj566 – Homework05 – Fouli...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: jiwani (amj566) – Homework05 – Fouli – (58395) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the value of f ′ (4) when f ( x ) = 1 3 x 3 / 2 − 6 x 1 / 2 . 1. f ′ (4) = 0 2. f ′ (4) = 1 2 3. f ′ (4) = − 1 4. f ′ (4) = 1 5. f ′ (4) = − 1 2 correct Explanation: Since d dx x r = rx r − 1 , we see that f ′ ( x ) = 1 2 x 1 / 2 − 3 x − 1 / 2 . At x = 4, therefore, f ′ (4) = − 1 2 . 002 10.0 points Determine the derivative of f when f ( x ) = parenleftbigg 1 3 parenrightbigg 2 / 3 . 1. f ′ ( x ) = 2 9 x − 1 / 3 2. f ′ ( x ) = 0 correct 3. f ′ ( x ) = 2 3 parenleftbigg 1 3 parenrightbigg − 1 / 3 4. f ′ ( x ) = parenleftbigg 1 3 parenrightbigg x − 1 / 3 5. f ′ ( x ) does not exist Explanation: The derivative of any constant function is zero. Consequently, f ′ ( x ) = 0 . 003 10.0 points Find the value of f ′ ( − 1) when f ( x ) = 9 x 8 − 9 x − 3 − 2 . Correct answer: − 45. Explanation: Since ( x n ) ′ = n · x n − 1 , holds for all integers n , we see that f ′ ( x ) = 72 x 7 + 27 x − 4 . Hence f ′ ( − 1) = − 45 . 004 10.0 points Determine the derivative of f when f ( x ) = √ 3 x + 1 √ 3 x . 1. f ′ ( x ) = 1 2 parenleftbigg 3 x + 1 x √ 3 x parenrightbigg 2. f ′ ( x ) = 1 2 parenleftbigg 3 x − 1 √ 3 x parenrightbigg 3. f ′ ( x ) = 3 x + 1 x √ 3 x 4. f ′ ( x ) = 1 2 parenleftbigg 3 x − 1 x √ 3 x parenrightbigg correct jiwani (amj566) – Homework05 – Fouli – (58395) 2 5. f ′ ( x ) = 3 x + 1 √ 3 x 6. f ′ ( x ) = 3 x − 1 x √ 3 x Explanation: Since d dx a x r = r a x r − 1 for all exponents r negationslash = 0 and constants a , we see that f ′ ( x ) = 1 2 radicalbigg 3 x − 1 2 1 x √ 3 x ....
View Full Document

## This note was uploaded on 07/10/2011 for the course KIN 321M taught by Professor Jensen during the Spring '11 term at University of Texas.

### Page1 / 6

Homework #5 - jiwani(amj566 – Homework05 – Fouli...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online