Find the Absolute Extreme Values of the Function on the Interval

question 210

Multiple Choice

Find the absolute extreme values of the function on the interval.
- $$f ( x ) = \ln ( x + 2 ) + \frac { 1 } { x } , 1 \leq x \leq 6$$

• A) Minimum value is \(- 1\) at \(x = - 1\); maximum value is \(\ln 8 + \frac { 1 } { 6 }\) at \(x = 6\)
• B) Minimum value is \(\ln 3 + 1\) at \(x = 1\); maximum value is \(\ln 8 + \frac { 1 } { 6 }\) at \(x = 6\)
• C) Minimum value is \(\ln 4 + \frac { 1 } { 2 }\) at \(x = 2\); maximum value is \(\ln 3 + 1\) at \(x = 1\)
• D) Minimum value is \(\ln 4 + \frac { 1 } { 2 }\) at \(x = 2\); maximum value is \(\ln 8 + \frac { 1 } { 6 }\) at \(x = 6\)

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Definitions:

Synapse

The junction between two neurons or between a neuron and a muscle where impulses pass by diffusion of a neurotransmitter.

Postsynaptic Membrane

The postsynaptic membrane is the region of a neuron that receives neurotransmitters from another neuron across the synaptic gap, playing a crucial role in neuron-to-neuron communication.

Synaptic Vesicle

A small, spherical sac that contains neurotransmitters, located within the terminal buttons of neurons, and is responsible for releasing neurotransmitters into the synaptic cleft.

Micrometer

A precision instrument used to measure small distances or thicknesses between two points, typically used in engineering and machining.