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If you have Calculus questions, please reply to this and post them here. We’ll check on a regular basis and try to answer them as quickly and accurately as possible. There’s just one condition. All story problems must include Sparkles the Unicorn. (e.g. If Sparkle’s tail grows at x rate, and his horn grows at half that rate at an angle of y degrees, how fast is the volume of his horn growing?)

And here’s our first problem!! Check the Answers tab above to check your answers.

1) Sparkles the Unicorn decided to have a birthday party for his mother. He ordered balloons for the party but to save money he decided to blow them up himself. He read the warning label and the label states that the balloon will burst when the diameter of the balloon reaches 16cm. Being a Unicorn, Sparkles can blow into the balloon at a constant 4cm^3/sec. At the moment the balloon bursts, how fast is the radius of the balloon increasing?

Another one to work on:

2)Sparkles lives in the tallest tower of the castle, and he wants to see the view of the beautiful Unicorn Meadow. Sparkles decides to install a square window, having a width of 80 cm. Sparkles is a clumsy unicorn, so there is a possibility that the width is off by up to 1 cm. Use differentials to estimate the maximum error possible in computing the area of the window.

3)Sparkles the Unicorn was up late last night finishing his physics trebuchet with Sunny the Leperchaun. He forgot to do his Calculus homework and the teacher is starting to collect last night’s assignment…Help Sparkles with the problems!

a) Find the absolute minimum

Y=x^(4)-x^(3)-x+1

b) Find the intervals of decrease and increase

Y=(x)/(x^(2)-4x+3)

c) Find the maximum on the interval [0,1]

Y=x^(1/3)-x

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I like the problems submitted so far. What do you think could be an appropriate topic from chapter 2 or 3?