Exam 4: Exponential and Logarithmic Functions

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Consider the function $f ( x ) = e ^ { - ( x - 6 ) ^ { 2 } / 5 }$ .For what value of x does this function attain its maximum value,and what is the maximum function value? Round maximum function value to two decimal places,if necessary.

(Multiple Choice)

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Question 21

Use logarithmic differentiation to find $f ^ { \prime } ( x )$ . $f ( x ) = \sqrt [ 8 ] { \frac { 6 x + 5 } { 8 + 6 x } }$

(Multiple Choice)

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Question 22

Determine the monthly car payment for a new car costing $18,228,if there is a down payment of $6,000 and the car is financed over a 6-year period at an annual rate of 9% compounded monthly.

(Multiple Choice)

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Question 23

Find all real numbers x that satisfy the given equation. $\left( \frac { 1 } { 81 } \right) ^ { x - 1 } = 3 ^ { 4 - 3 x ^ { 2 } }$

(Multiple Choice)

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Question 24

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Consider the function $f ( x ) = e ^ { - ( x - 6 ) ^ { 2 } / 5 }$ .For what value of x does this function attain its maximum value,and what is the maximum function value? Round maximum function value to two decimal places,if necessary.

Use logarithmic differentiation to find $f ^ { \prime } ( x )$ . $f ( x ) = \sqrt [ 8 ] { \frac { 6 x + 5 } { 8 + 6 x } }$

Determine the monthly car payment for a new car costing $18,228,if there is a down payment of $6,000 and the car is financed over a 6-year period at an annual rate of 9% compounded monthly.

Find all real numbers x that satisfy the given equation. $\left( \frac { 1 } { 81 } \right) ^ { x - 1 } = 3 ^ { 4 - 3 x ^ { 2 } }$

Functions,graphs,and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

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Exam 4: Exponential and Logarithmic Functions

Consider the function f(x)=e−(x−6)2/5f ( x ) = e ^ { - ( x - 6 ) ^ { 2 } / 5 }f(x)=e−(x−6)2/5 .For what value of x does this function attain its maximum value,and what is the maximum function value? Round maximum function value to two decimal places,if necessary.

Use logarithmic differentiation to find f′(x)f ^ { \prime } ( x )f′(x) . f(x)=6x+58+6x8f ( x ) = \sqrt [ 8 ] { \frac { 6 x + 5 } { 8 + 6 x } }f(x)=88+6x6x+5​​

Determine the monthly car payment for a new car costing $18,228,if there is a down payment of $6,000 and the car is financed over a 6-year period at an annual rate of 9% compounded monthly.

Find all real numbers x that satisfy the given equation. (181)x−1=34−3x2\left( \frac { 1 } { 81 } \right) ^ { x - 1 } = 3 ^ { 4 - 3 x ^ { 2 } }(811​)x−1=34−3x2

Functions,graphs,and Limits

Differentiation: Basic Concepts

Additional Applications of the Derivative

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Consider the function $f ( x ) = e ^ { - ( x - 6 ) ^ { 2 } / 5 }$ .For what value of x does this function attain its maximum value,and what is the maximum function value? Round maximum function value to two decimal places,if necessary.

Use logarithmic differentiation to find $f ^ { \prime } ( x )$ . $f ( x ) = \sqrt [ 8 ] { \frac { 6 x + 5 } { 8 + 6 x } }$

Find all real numbers x that satisfy the given equation. $\left( \frac { 1 } { 81 } \right) ^ { x - 1 } = 3 ^ { 4 - 3 x ^ { 2 } }$