Gradient of the Tangent

• A

• B

• C

• D

The derivative of a function is its

• Slope

• Maximum/Minimum

• Instantaneous rate of change

• Common Denominator

For what values of x does f(x) have a horizontal tangent?

• -3.5, 3.5

• -5, 5

• there are no horizontal tangents

• -5, 0, 5

According to the graph, at the point x=-2, is f(x) increasing or decreasing and why?

• At x=-2 f(x) is increasing because the graph has a positive slope.

• At x=-2 f(x) is decreasing because the graph has a positive slope.

• At x=-2 f(x) is decreasing because the graph lies below the x-axis.

• At x=-2 f(x) is decreasing because the graph has a negative slope

Given f(x) = 3x²+2x, find the gradient of the tangent where x = - 3.

• 12

• -4

• 10

• -16

Order the derivatives of each point on the graph from least to greatest.

• ABC

• BCA

• CBA

• BAC

Which one of the following statements is always true?

• When a graph is increasing, its derivative is negative.

• When a graph is decreasing, so is its derivative.

• When a graph is decreasing, its derivative is negative.

• When a graph is increasing, so is its derivative.

If a function has a derivative that is negative, what does that tell you?

• The function is increasing

• The function is decreasing

Find the gradient of f(x) = -3x² – 6x at x = 1.

• m = 0

• f'(x) = -6x - 6

• f'(x) = 6x

• m = -12

Find the derivative of f(x) = 5x² + 7x - 3.

• 2x + 7

• 10x + 7

• 10x + 4

• 2x + 4