Stationary Points Quiz

What is a stationary point?

• A stationary point is a point on a curve where the gradient is undefined.

• A stationary point is a point on a curve where the gradient is negative.

• A stationary point is a point on a curve where the gradient is zero.

• A stationary point is a point on a curve where the gradient is positive.

How do you find the stationary points of a quadratic function?

• Find the integral and set it equal to zero

• Find the second derivative and set it equal to zero

• Find the maximum value and set it equal to zero

• Find the derivative and set it equal to zero

How do you find the stationary points of a cubic function?

• Find the derivative and set it equal to zero

• Find the second derivative and set it equal to zero

• Take the integral and set it equal to zero

• Substitute different values of x and find the corresponding y values

How do you find the stationary points of a rational function?

• Take the integral of the function and set it equal to zero to find the x-values of the stationary points.

• Find the average rate of change of the function to locate the stationary points.

• Graph the function and identify the x-values where the graph is horizontal.

• Take the derivative of the function and set it equal to zero to find the x-values of the stationary points.

What is the nature of stationary points?

• Stationary points can only be maximum.

• Stationary points can be maximum, minimum, or points of inflection.

• Stationary points can only be minimum.

• Stationary points can only be points of inflection.

What is the second derivative test?

• The second derivative test is used to find the area under a curve.

• The second derivative test is used to find the derivative of a function.

• The second derivative test is a method used in calculus to determine the nature of critical points of a function.

• The second derivative test is used to find the maximum value of a function.

When is a stationary point a local maximum?

• When the second derivative changes from negative to positive.

• When the second derivative is positive.

• When the second derivative is negative.

• When the second derivative is zero.

When is a stationary point a local minimum?

• When the second derivative is positive.

• When the second derivative is negative.

• When the second derivative is a quadratic.

• When the second derivative is zero.

At a point of inflection..

• The second derivative is zero

• The second derivative is positive

• The second derivative is negative

• The second derivative is impossible to find

What is the second derivative of the quadratic function ax^2 + bx + c?

• 0

• a

• 3

• 2a