Understanding Rate of Change in Triangles

The video tutorial explains how to determine the rate of change of the area of a triangle when its base is decreasing and its height is increasing. It begins by identifying the units of various expressions and the given values. The tutorial then uses the product rule to derive the rate of change of the area, providing a step-by-step solution to the problem.

What is the main task described in the problem?

• To find the rate of change of the area of the triangle.

• To find the rate of change of the base of the triangle.

• To find the rate of change of the height of the triangle.

• To find the rate of change of the perimeter of the triangle.

What are the units for the rate of change of the base?

• Meters

• Meters per hour

• Square meters

• Hours

What is the unit for the area of the triangle?

• Meters

• Meters per hour

• Square meters

• Hours

What is the given rate of change for the base of the triangle?

• -13 meters per hour

• -6 meters per hour

• 6 meters per hour

• 13 meters per hour

What is the height of the triangle at time t sub 0?

• 5 meters

• 1 meter

• 13 meters

• 6 meters

Which mathematical rule is used to derive the formula for the rate of change of the area?

• Chain rule

• Quotient rule

• Power rule

• Product rule

What is the expression for the rate of change of the area using the product rule?

• a'(t) = b(t) * h(t)

• a'(t) = b'(t) * h'(t)

• a'(t) = 1/2 * (b'(t) * h(t) + b(t) * h'(t))

• a'(t) = b(t) * h'(t) + h(t) * b'(t)

What is the rate of change of the height of the triangle?

• 6 meters per hour

• 13 meters per hour

• -13 meters per hour

• -6 meters per hour

What is the value of b(t) at time t sub 0?

• 6 meters

• 1 meter

• 13 meters

• 5 meters

What is the final step to find the rate of change of the area?

• Calculate the perimeter of the triangle.

• Plug in the given values into the derived formula.

• Use the chain rule to differentiate.

• Find the average of the base and height.