Related Rates
Read this topicExplanations 11
- Related rates problems analyze the rate at which functions change for certain instances in time. These problems generally involve two or more functions where you relate the func…
By Joshua Siktar
- "Related rates" problems, as the heading suggests, deal with functions that can be expressed in terms of one another. We might know that y=f(x)y = f(x)y=f(x), where both yyy and…
By Alexander Mason, Alex Federspiel
- Related rates are an application of implicit, or partial, differentiation. These are dependent and related rates because the final answer will rely on two or more variables, so …
By Lily Zacharias, Alex Federspiel
- (Video) Related Rates: Ships and Distance by PatrickJMT Here's a video by patrickJMT showing you how to solve related rate problems. Despite having some nice alliteration, relat…
By Alex Federspiel
- (Video) Related Rates: Cones by PatrickJMT Here's another video by patrickJMT where he shows you how to solve a related rates problem involving cones. The problem says: Gravel i…
By Alex Federspiel
- (Video) Related Rates: Point on a Graph by PatrickJMT Here's another video by patrickJMT on related rates. This one deals with a point moving on a graph. The problem says: A poi…
By Alex Federspiel
- (Video) Related Rates: Trigonometry by PatrickJMT Here's another video by patrickJMT where he looks at a related rates problem which involves trig. The problem states: In the ri…
By Alex Federspiel
- (Video) Related Rates: Baseball! by PatrickJMT Here's another video by patrickJMT dealing with related rates. The problem states: A baseball diamond is a square with side 909090…
By Alex Federspiel
- (Video) Related Rates: Circumference by PatrickJMT Here's another video by patrickJMT going over a related rates word problem. This one deals with the change in a circles circum…
By Alex Federspiel
- (Video) Related Rates: Sliding Ladder by PatrickJMT Here's another video by patrickJMT showing you how to solve a related rates problem involving a sliding ladder. The problem s…
By Alex Federspiel
- (Video) Related Rates: Traveling Cars by PatrickJMT Here's the final video by patrickJMT on related rates. This one deals with cars traveling from an intersection. The problem s…
By Alex Federspiel
Problems 11
- A circle of radius 2 cm2\ \textrm{cm}2 cm has area increasing at 8π cm2/sec8\pi \ \textrm{cm}^2/\textrm{sec}8π cm2/sec. How fast is the radius changing, in cm/sec\textrm{cm}/\te…
- If the volume of a cube is decreasing at 6 m3/sec6 \ \textrm{m}^3/\textrm{sec}6 m3/sec, what is the rate of change of the surface area of the cube when the surface area is 24 m2…
- A cylindrical water bottle with radius 5 cm5 \ \textrm{cm}5 cm is being filled with tea at a rate of 5π cm3/sec5\pi \ \textrm{cm}^3/\textrm{sec}5π cm3/sec. How fast is the heigh…
- A triangle has altitude increasing at 3 cm/min3 \ \textrm{cm}/\textrm{min}3 cm/min while its area is increasing at 4 cm2/min4\ \textrm{cm}^2/\textrm{min}4 cm2/min. At what rate …
- A 131313-meter long ladder rests against a vertical wall. If the top of the ladder slides downward at 2 m/s2 \ \textrm m / \textrm s2 m/s, how fast is the bottom of the ladder s…
- A perfectly spherical panda fattens so that its volume increases at 4π4\pi4π cubic meters per year. Find the rate of change of its diameter (in meters/year) when it is 2 meters …
- Shannon saved a special snowball to throw at her friend Doug. Sadly, she noticed that its surface area was decreasing at a rate of 0.5 cm2/min0.5\text{ cm}^2/\text{min}0.5 cm2/m…
- Bianca is outside flying her brand new kite. The kite is 75 ft75\text{ ft}75 ft off the ground and is moving horizontally at a speed of 16 ft/sec16\text{ ft/sec}16 ft/sec. At wh…
- Jasmine is filling a trough with water for her horses. The trough is 16 ft16\text{ ft}16 ft long and its ends are isosceles triangles that are 4 ft4\text{ ft}4 ft across at the …
- Haley and Penelope are trying to locate each other at an amusement park. Haley is walking north of the carousel at 5 ft/sec5\text{ ft/sec}5 ft/sec. Five minutes later Penelope s…
- You have your perfectly cylindrical, magical bucket. It's magical because the radius of any liquid inside is always one-fourth of its height. The bucket itself is is 36 in36\tex…