Applications of Derivative Quiz #1

The tangent line passing through the critical points are parallel to the x-axis.

• True

• False

• Neither

The tangent line passing through the critical points are parallel to the y-axis.

• True

• False

• Neither

Find the maximum(s) of the function f(x) = sin x + cos² x on 0 < x < 2π.

• 1

• -1

• 5/4

• No local max

Find the minimum(s) of the function f(x) = sin x + cos² x on 0 < x < 2π.

• 1

• -1

• 5/4

• No local min

What are the critical points for f(x) on 0 < x < 2π.

• π/2

• (3π)/2

• π/6

• (5π)/6

• 0

Find the critical points of f(x) = 2x³-15x²+24x+7.

• x = 0

• x = 1

• x = 4

• x = 6

Find the critical point(s) of f(x) = 1 - (x - 1)^2/3.

• x = -1

• x = 0

• x = 1

• x = 2

If f'(c) > 0, f is __ on that interval.

• increasing

• decreasing

• constant

• none of these

If f'(c) < 0, f is __ on that interval.

• increasing

• decreasing

• constant

• none of these

Mark the test points that can be used to determine the intervals where the function f(x) = x³ - 3x² -24x + 32 is increasing and decreasing.

• -3

• 0

• 4

• 5