15. Consider the function f(x) = 2x^3 - 3x^2

15. Consider the function $f(x) = 2x^3 - 3x^2 - 36x$. a) What is the maximum number of local extrema this function can have? Explain. b) What is the maximum number of points of inflection this function can have? c) Find and classify the critical points. Identify the intervals of increase and decrease, and state the intervals of concavity. d) Sketch the function.

Consider the following Function Y= x^3/3 +x^2/2 -2x +1 (a) Find y' = f '(x). f '(x) = _____________ (b) Find the critical values. (Enter your answers as a comma-separated list.) x = ___________________ (c) Find the critical points. (x,y) = __________________ (smaller x-Value) (x,y) = __________________ (Larger x-Value) (d) Find intervals of x-values where the function is increasing. (Enter your answer using interval notation.) ___________________________ Find intervals of x-values where the function is decreasing. (Enter your answer using interval notation.) ___________________________ (e) Classify the critical points as relative maxima, relative minima, or horizontal points of inflection. In each case, check your conclusions with a graphing utility. (If an answer does not exist, enter DNE.) relative maxima (x,y) = ___________________ relative Minima (x,y) = ___________________ horizontal points of inflection (x,y) = ___________________

Likhit G.

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