Warm up 1. Calculate the area of a circle with diameter 24 ft. 2. If a right triangle has sides 6 and 9, how long is the hypotenuse? 3. Take the derivative with respect to x. 4.Now take the derivative with respect to t.

4.1 Related Rates  Focus: calculate related rates.

4.1 Related Rates  Ex: A fire starts in a dry field and spreads in the form of a circle. The radius of the circle increases at a rate of 6 ft/min. Find the rate at which the fire area is increasing when the radius is 150 ft. (Notice that this question relates feet and time together as a rate.)

A fire starts in a dry field and spreads in the form of a circle. The radius of the circle increases at a rate of 6 ft/min. Find the rate at which the fire area is increasing when the radius is 150 ft. Steps To Attack a Related Rates Problem 1. Write down all given information R

A fire starts in a dry field and spreads in the form of a circle. The radius of the circle increases at a rate of 6 ft/min. Find the rate at which the fire area is increasing when the radius is 150 ft. Steps To Attack a Related Rates Problem 2. Write a unifying equation. (you might have to do some substitutions.)

A fire starts in a dry field and spreads in the form of a circle. The radius of the circle increases at a rate of 6 ft/min. Find the rate at which the fire area is increasing when the radius is 150 ft. Steps To Attack a Related Rates Problem 3. Differentiate with respect to time.

A fire starts in a dry field and spreads in the form of a circle. The radius of the circle increases at a rate of 6 ft/min. Find the rate at which the fire area is increasing when the radius is 150 ft. Steps To Attack a Related Rates Problem 4. Solve for what is asked.

Types of related rates problems 1. No context, just an equation. 2. Geometry 3. Pythagorean 4. Angle of elevation (we will do these later)

1. No Context.

A conical tank is being filled at a rate of 25 cubic feet per minute. The tank is 12 feet high and a diameter of 10 feet. Find what rate the height is changing when the water is 8 feet deep? 2. Geometry

A 13 ft. ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/sec. How fast will the foot be moving away from the wall when the top is 5 ft. above the ground? 3. Pythagorean Type.

A spherical balloon is being deflated so that its radius is being decreased a constant rate of 15 cm/min. At what rate must the air be removed when the radius is 9 cm? 2. Geometry Type.

ASGN 35 p odd 1. geo, just derivative 3. Geometry 5. No context 7. No context 9. Geometry 11. Pythag.