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# Derivatives

### Polynomials and second derivatives

Find a polynomial p so that: p''(t)+3p'(t) + 2p(t) = (t^2)-2 for all numbers t. (note: p''= p double prime and t^2 = t raised to the power of 2)

### Absolute Maximum and Minimum of a Given Function

Find the absolute maximum and absolute minimum values of f on the given interval. F(x) = sqrt(9-x^2) [-1, 2] or in other words: F(x) equals the square root of (9 minus x squared). The problem is also attached in MS word.

### Using related rates to answer a pulley question.

Two carts A and B are connected by a rope 39 feet long that passes over pulley P. The point Q is on the floor directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 2 ft/sec. How fast is cart B moving toward Q at the instant cart A is 5 feet from Q? Express solution using related rate n

### Limits and derivatives

Find the derivative. a) f= 4-sqrt(x+3) b) f= (x+1)/(2-x) See attachment below for additional information.