Differentiation

Multiple Choice

Differentiate with respect to x...

• 6x² + 6x

• 6x + 2

• 6x + 6

• 6x² + 6

Multiple Choice

Differentiate with respect to x...

• 16x + 4x^-2

• 16x - 4x^-2

• 16x + 4x

• 16x - 4x

Multiple Choice

Differentiate with respect to x...

• x² + x

• x² - x

• x² + x³

• x² - x^-3

Multiple Choice

Differentiate with respect to x...

• x² + x

• x² - x

• x² + x³

• x² - x^-3

​Increasing:

​A function is increasing at any time when the graph of the function "rises from left to right", or in other words, the y-values increases while the x-values increases, creating a positive slope (rate of change).

​

​- The function to the right is increasing shown in the yellow interval.

​Decreasing:

​A function is decreasing at any time when the graph of the function "falls from left to right", or in other words, the y-values decreases while the x-values increases, creating a negative slope (rate of change).

​

The function to the right is decreasing shown by the orange interval.

Multiple Choice

When is this function increasing?

• −2.5 < x < 2.5
• 0 < x < 5
• 0 < x < 55
• −5 < x < 0