Answer to Question #64110 in Calculus for Mai

Question

1.Suppose that for all x >= 0, the average value of f(x) on [0; x] is equal to x. What is the
funtion f(x)?
2.The equation x^4+x^3-4 = 0 has a solution near x = 1. Use Newton's method to find this
solution correct to 8 signficant figures.
3.At a certain moment, a triangle has base length 10 cm and perpendicular height 8 cm. The
length is increasing at a rate of 1 cm/s while the height is decreasing at 1 cm/s. How fast is the
area changing? Is the area increasing or decreasing?