Curves - AP Calculus AB

To find local extrema (if any), set the derivative equal to 0 and solve for .

Here, , so .

However, this function is a parabola (since it is quadratic) and concave up (since the coefficient of the quadratic term is positive), and therefore has no local maximum -- only a local minimum.

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema (if any), set the derivative equal to 0 and solve for .

Here, , so .

However, this function is a parabola (since it is quadratic) and concave up (since the coefficient of the quadratic term is positive), and therefore has no local maximum -- only a local minimum.

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema (if any), set the derivative equal to 0 and solve for .

Here, , so .

However, this function is a parabola (since it is quadratic) and concave up (since the coefficient of the quadratic term is positive), and therefore has no local maximum -- only a local minimum.

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema (if any), set the derivative equal to 0 and solve for .

Here, , so .

However, this function is a parabola (since it is quadratic) and concave up (since the coefficient of the quadratic term is positive), and therefore has no local maximum -- only a local minimum.

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema (if any), set the derivative equal to 0 and solve for .

Here, , so .

However, this function is a parabola (since it is quadratic) and concave up (since the coefficient of the quadratic term is positive), and therefore has no local maximum -- only a local minimum.

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema (if any), set the derivative equal to 0 and solve for .

Here, , so .

However, this function is a parabola (since it is quadratic) and concave up (since the coefficient of the quadratic term is positive), and therefore has no local maximum -- only a local minimum.

To find local extrema (if any), set the derivative equal to 0 and solve for .

Here, , so .

However, this function is a parabola (since it is quadratic) and concave up (since the coefficient of the quadratic term is positive), and therefore has no local maximum -- only a local minimum.

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema (if any), set the derivative equal to 0 and solve for .

Here, , so .

However, this function is a parabola (since it is quadratic) and concave up (since the coefficient of the quadratic term is positive), and therefore has no local maximum -- only a local minimum.

To find local extrema, use the first derivative test.

Here, , so or .

Test points in each of the intervals defined by those potential extrema. For example, (increasing), (decreasing), and (increasing).

Since the function increases up to , then decreases, is a local maximum. (For completeness, is a local minimum, not a maximum.)

To find local extrema (if any), set the derivative equal to 0 and solve for .

Here, , so .

However, this function is a parabola (since it is quadratic) and concave up (since the coefficient of the quadratic term is positive), and therefore has no local maximum -- only a local minimum.