Analytical Applications of Differentiation

Evaluate the fourth derivative at a point and check its sign

Evaluate the second derivative at a point and check its sign

Evaluate the third derivative at a point and check its sign

Evaluate the first derivative at a point and check its sign

All non-negative real numbers

All positive real numbers

All negative real numbers

All real numbers

1. Determine if there are any discontinuities, 2. Find the domain, 3. Find the x- and y-intercepts, 4. Find the extrema of the function, 5. Find the symmetry of the function, 6. Find the points of inflection and concavity, 7. Find the asymptotes.

1. Find the domain, 2. Determine if there are any discontinuities, 3. Find the x- and y-intercepts, 4. Find the symmetry of the function, 5. Find the extrema of the function, 6. Find the points of inflection and concavity, 7. Find the asymptotes.

1. Find the extrema, 2. Determine the domain, 3. Find the points of inflection, 4. Determine if there are any discontinuities, 5. Find the x- and y-intercepts, 6. Find the symmetry of the function, 7. Find the asymptotes.

1. Determine if there are any discontinuities, 2. Find the domain, 3. Find the extrema, 4. Find the symmetry of the function, 5. Find the x- and y-intercepts, 6. Find the points of inflection, 7. Find the asymptotes.

The x-coordinate of the critical point

The y-coordinate of the critical point

The slope of the tangent line

The direction of concavity

Local minimum

Local maximum

Symmetry

Point of inflection

The x-intercept

The point of inflection

The domain of the function

The local maximum or minimum

Replace all x's in the function with a -x, and if the function remains unchanged, it has even symmetry.

Replace all x's in the function with a -x, and if the function becomes its negative, it has even symmetry.

Evaluate the second derivative at a point, and if it equals zero, the function has even symmetry.

Evaluate the first derivative at a point, and if it equals zero, the function has even symmetry.

Domain and y-intercepts

Extrema and asymptotes

Discontinuities and extrema

Symmetry and points of inflection

It has no local extrema

It is a linear function

It has no critical points

It is not continuous

Odd symmetry

Horizontal symmetry

No symmetry

Even symmetry