Review for Exam #2

# Review for Exam #2 - jiwani(amj566 – Review Exam 02 –...

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) – Review Exam 02 – Fouli – (58395) 1 This print-out should have 32 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The cost function for Levi Strauss to pro- duce x pairs of blue jeans is C ( x ) = 1600 + 5 x- 9 100 x 2 + 1 1250 x 3 . Find the marginal cost to Levi Strauss of producing 100 pairs of blue jeans. 1. marginal cost = \$9 per pair 2. marginal cost = \$10 per pair 3. marginal cost = \$7 per pair 4. marginal cost = \$8 per pair 5. marginal cost = \$11 per pair correct Explanation: By definition, the Marginal cost is the derivative, C ′ ( x ), of the cost function C ( x ). Now C ′ ( x ) = 5- 9 50 x + 3 1250 x 2 . When x = 100, therefore, marginal cost = C ′ (100) = \$11 per pair . 002 10.0 points TI has discovered that the total cost (in dollars) of producing x calculators per day is given by C ( x ) = 800 + 60 x- x 2 5 . Find the Marginal Cost to TI at a production level of x calculators. 1. Marginal Cost = C ′ ( x ) = 60 + 2 5 x 2. Marginal Cost = 60 + 1 5 x 3. Marginal Cost = C ( x ) x 4. Marginal Cost = C ( x + 1)- C ( x ) 5. Marginal Cost = 60- 1 5 x 6. Marginal Cost = C ′ ( x ) = 60- 2 5 x correct Explanation: The Marginal cost by definition is the derivative, C ′ , of the Cost function C . Thus Marginal Cost = 60- 2 5 x . 003 10.0 points Find the derivative of f when f ( x ) = 5 x cos 6 x . 1. f ′ ( x ) = 5 cos5 x- 5 x sin6 x 2. f ′ ( x ) = 30 cos 6 x + 6 x sin 6 x 3. f ′ ( x ) = 5 cos6 x- 30 x sin 6 x correct 4. f ′ ( x ) = 30 cos 6 x- 5 x sin 6 x 5. f ′ ( x ) = 5 cos6 x + 30 x sin 5 x Explanation: Using the formulas for the derivatives of sine and cosine together with the Chain Rule we see that f ′ ( x ) = (5 x ) ′ cos 6 x + 5 x (cos 6 x ) ′ = 5 cos6 x- 30 x sin 6 x . 004 10.0 points jiwani (amj566) – Review Exam 02 – Fouli – (58395) 2 Find the derivative of f ( x ) = 3 x sin4 x + 3 4 cos 4 x . 1. f ′ ( x ) = 12 x cos 4 x + 6 sin4 x 2. f ′ ( x ) = 12 x cos 4 x- 6 sin4 x 3. f ′ ( x ) = 12 cos 4 x 4. f ′ ( x ) = 12 x cos 4 x correct 5. f ′ ( x ) =- 12 x cos4 x Explanation: Since d dx sin x = cos x, d dx cos x =- sin x, it follows that f ′ ( x ) = 3 sin4 x + 12 x cos 4 x- 3 sin 4 x. Consequently, f ′ ( x ) = 12 x cos 4 x . 005 10.0 points Find the equation of the tangent line to the graph of 4 y 2- xy- 9 = 0 , at the point P = (9 , 3). 1. 3 y = x 2. 14 y = 3 x + 15 3. 14 y + 3 x = 15 4. 5 y = x + 6 correct 5. 5 y + x = 6 Explanation: Differentiating implicitly with respect to x we see that 8 y dy dx- y- x dy dx = 0 , so dy dx = y 8 y- x . At P = (9 , 3), therefore, dy dx vextendsingle vextendsingle vextendsingle P = 1 5 ....
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 / 17

Review for Exam #2 - jiwani(amj566 – Review Exam 02 –...

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

View Full Document
Ask a homework question - tutors are online