Engineering Board Exam Reviewer · Related Rates (Time Rates) · medium
A point moves along the curve y=x2 so that x increases at 3 units per second. How fast is the distance from the origin to the point increasing when x=1?
- 4.24 units/s
- 9 units/s
- 6.36 units/s
- 3 units/s
Answer
C. 6.36 units/s
Solution
D2=x2+y2=x2+x4. Differentiate: 2DdD/dt=(2x+4x3)dx/dt. At x=1: D= 2, so dD/dt=(2+4)(3)/2 2=18/2 2 6.36 units/s.
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