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Calculus help pls?!?
1. Consider the polynomial
p(x) = K(x^2 − 16)(x − a)
where a and K are constants. Suppose that p(0) = 12, and p(x) has an inflection point at x = 1/3.
(a) Find the values of constants a and K.
(b) Find and classify all critical points of the polynomial p(x).
(c) Which critical point is a maximum?
2. Given the function f(x) = (x^3)/(1-x^2)
(a) Does f(x) have any asymptotes? Justify your answer.
(b) Determine all intervals where f(x) is increasing and where it is decreasing.
Locate and classify all critical points and local extrema of f(x).
2 Answers
- 3 years ago
Here's some facts for you:
* A function g(x) is increasing when g'(x) > 0
and decreasing when g'(x) < 0.
* If g'(x) = 0, then x is called a critical point.
The critical point x is a local max if g''(x) < 0 and a local min if g''(x) > 0
* An inflection point means that g''(x) = 0.
* an asymptote occurs when a function gets arbitrarily close to a line. For the function in 2), this occurs as x approaches +-1. Can you see why?
- ted sLv 73 years ago
p(0) = 12 means 16 a K = 12........p ' ' ( 13) = 0 means a = 1 ---> K = 12...........p ' = 0 yields x = - 2 & 16 / 6....local max then min...{ it is a cubic }..........yes ..x = ± 1.....f(x) = - x + x / (1-x²).....increasing when ( 1 + x ) / ( 1 - x²)² > 1