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Find the maximum and minimum value of f(x) =40/3x4+8x3-18x2+60..... ..Please provide final answer with reason

Find the maximum and minimum value of f(x) =40/3x4+8x3-18x2+60..... ..Please provide final answer with reason

Grade:12th pass

1 Answers

Arun
25758 Points
3 years ago
Dear student
 
It can be assumed as f(x) = 1/g(x)
 
Now
 
If g(x) is increasing then f(x) is decresing and vice-versa.
 
For g(x)
 
g'(x) = 12x³ + 24x² - 36 x = 12x ( x² + 2x -3) = 12 x( x+3) (x-1)
 
Hence
 
g(x) is negative for (- infinity , -3) and (0, 1)
 
Hence here f(x) is increasing and for x belongs to ((-3 , 0) and (1, infinity) it is decreasing

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