Derivative Skills 2.1 to 2.4 Practice

Find the derivative of the given equation:

f(x) = x⁴ + 4x³ - 2x²

• f'(x) = x³ + x² - x

• f'(x) = 4x³ + 12x² + 4x

• f'(x) = 4x + 12x - 4x

• f'(x) = 4x³ + 12x² - 4x

Differentiate h(x) = 3x^5/3 - 6x^1/6 + 3x

• h'(x) = 5x^2/3 - x^-5/6 + 3

• h'(x) = 3x^2/3 - 6x + 3

• h'(x) = 5x^4/3 - 6x + 3

• h'(x) = 3x^4/3 - x^-5/6 + 3

At which point(s) will the slope(s) of the tangent line be POSITIVE?

• At C only

• At points A, C, and E only

• At points B and D only

• At points A and E only

Where on this graph would you find a horizontal tangent line?

• x = -3

• x = 0

• x = 3

• There are no horizontal tangent lines on this graph

For which value(s) of x is the function continuous but not differentiable?

• x = -1

• x = 0

• x = 2

• x = 3, x = -2

For what values of x in the domain of the above function does the function appear to be differentiable?

• (-2, 3)

• All real numbers.

• [-2, 3]

The function shown:

• Is continuous at x = 8

• Is differentiable at x = 8

• Has a limit that exists at x = 8

• Exists at x = 8

Tags

CCSS.HSF-IF.C.7B

The function shown:

• Is continuous at x = 2

• Is differentiable at x = 2

• Has a limit that exists at x = 2

• Exists at x = 2

Tags

CCSS.HSF-IF.C.7B

The function shown:

• Is continuous at x = 4

• Is differentiable at x = 4

• Has a limit that exists at x = 4

• Exists at x = 4

Tags

CCSS.HSF-IF.C.7B