Question

A method for determining whether a critical point is a minimum, maximum, or neither using the slope of the curveA) First Derivative TestB) Absolute MaximumC) AccelerationD) Concavity

Answer 1

Answer:

a. First derivative

Step-by-step explanation:

To determine the nature of the stationary points:

Either  Find  dy/dx or d2y/dx2

If the result is: positive—the point is a minimum one; negative—the point is a maximum one; zero—the point is a point of inflexion

or

Determine the sign of the gradient of the curve just before and just after the stationary points.

If the sign change for the gradient of the curve is: positive to negative—the point is a maximum one; negative to positive—the point is a minimum one; positive to positive or negative to negative— the point is a point of inflexion

Answer 2

A method for determining whether a critical point is a minimum, maximum, or neither using the slope of the curve is the First Derivative Test (Letter A).

First Derivative Test

Critical  points  represent the values of x for that f '(x) is zero or the derivative doesn't exist.  Therefore, they represent the only places where a function can have a local minimum, maximum or neither using the slope of the curve. See the rules for this method:

• If f′(x) changes from positive to negative at c, then f(c) is a local maximum.

• If f′(x) changes from negative to positive at c, then f(c) is a local minimum.
• If f′(x) does not change sign at c, then f(c) is neither a local maximum or minimum.

Read more about the First Derivative Test here:

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