The Lagrange Multipliers Needed to Find the Maximum and Minimum $f ( x , y ) =$

question 43

Essay

The Lagrange multipliers needed to find the maximum and minimum values of $f ( x , y ) =$ 8xy on the circle $x ^ { 2 } + y ^ { 2 } = 25$ is $\lambda = \pm 4$ , where $\nabla f = \lambda \nabla g$ .Estimate the maximum and minimum values of 8xy subject to the constraint $x ^ { 2 } + y ^ { 2 } = 30.25$ .

Comprehend the role of the scientific method in psychology and contrast it with common sense and subjective experiences.

Understand the role of health psychologists in studying factors influencing health and illness.

Distinguish between various psychological specialties based on their focus areas.

Recognize consistent patterns in behavior and mental processes as key assumptions in psychology.

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Definitions:

Systematic Desensitization

A therapy technique used to treat phobias and anxiety by gradually exposing the person to the anxiety source in a controlled environment.

Muscle Relaxation

A technique used to alleviate stress or tension in the muscles through exercises, often involving the deliberate tension and then relaxation of specific muscle groups.

Social Skills Training

A behavior therapy designed to improve interpersonal skills that emphasizes modeling, behavioral rehearsal, and shaping.

Interpersonal Behaviors

The actions or reactions exhibited by individuals towards others in social situations, influencing the nature and quality of relationships.