Applications of Derivatives worksheets
Applications of Derivatives worksheets give students in Calculus I focused practice in applications of derivatives. This page has 1 free printable sets, grouped by grade, and every set includes a computed answer key that is never wrong. Print them or save as a PDF, no login needed.
What's inside
- The radius of a circular oil slick grows at a constant 3 cm/min. How fast is the area increasing at the instant the radius is 4 cm? Give an exact answer in terms of π.
- A spherical balloon is inflated so its radius increases at 3 cm/s. How fast is the volume increasing when the radius is 6 cm? Give an exact answer in terms of π.
- A 10 ft ladder leans against a vertical wall. The bottom slides away from the wall at 3 ft/s. How fast is the top of the ladder sliding down the wall when the bottom is 6 ft from the wall?
- Each edge of a cube of ice melts (shrinks) at 3 mm/min. How fast is the volume decreasing when each edge is 2 mm?
- Water is poured into a conical tank so the water level rises at 2 cm/min. At every depth the water surface's radius is half the water's depth. How fast is the volume of water increasing when the depth is 10 cm? Give an exact answer in terms of π.
- The radius of a circular oil slick grows at a constant 1 cm/min. How fast is the area increasing at the instant the radius is 10 cm? Give an exact answer in terms of π.
Sample questions. Each set (A, B, C…) has fresh numbers and a computed answer key.
Calculus I Applications of Derivatives
Frequently asked questions
Are these applications of derivatives worksheets free?
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Do the worksheets have answer keys?
Yes, free, on every sheet. The answers are computed in code from the exact questions on the page, and the key prints on a page of its own so the student sheet stays clean.
What grades do applications of derivatives worksheets cover?
Applications of Derivatives worksheets on this page cover Calculus I. There are 1 printable sets in total, grouped by grade so you can pick the right level.
How do I print or download them?
Open any set, then use your browser's print option to print it or to save it as a PDF. The pages are laid out to print cleanly on standard letter or A4 paper.