Math141Tes#2_anotheroldone

Math141Tes#2_anotheroldone - Hint: You want to take the...

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Math 141 Test#2 from another teacher 1. Use the definition of derivative of the function below. In other works, find the derivative of the function below “the long way”. x x x f + = ) ( 2. Use the graph below of the derivative to answer the following questions about the original function, f(x). (I’ll draw on the board) a. On what interval(s) is f(x) decreasing? b. On what interval(s) is f(x) concave up? c. List all the x-values where f(x) has a local maximum. d. List one x-value where f(x) has an inflection point? 3. Explain how continuity and differentiability are related. In other words, if a function is continuous, what do we know about the differentiability of the function , and vice versa. 4. Use the product rule and chain rule to prove the quotient rule.
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Unformatted text preview: Hint: You want to take the derivative of a function like: ) ( ) ( x g x f 5. Find the derivative of each of the following; you do not need to simplify. a. 2 1 4 ) ( 3 + + +--= x x x x x f b. 1 2 5 ) ( + = t t g c. ) arctan( ) 1 ( ) ( 2 x x x h + = d. ) ( sin ) cos( ) ( 2 2 u u u r + = e. t t t f ) ln( ) ( = 6. Use implicit differentiation to find the derivative of the following: 2 2 x xe y y + = 7. Use your answer from the previous problem to find the equation of the tangent line at point (-2, 0). 8. Use logarithmic differentiation to find the derivative of the following. x y y e x 2 = 9. Let x xe x g = ) ( Find the nth derivative of g(x)....
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