Question

Enumerate the steps to determine maxima or minima of a function with example. Identify maximum or minimum au
of function Y 12 30x5X2​

Answer 1

steps to determine maxima or minima of a function

Step-by-step explanation:

y = f(x)

find derivative

y' = f'(x)

Equate with 0

f'(x) = 0

find all values of x

then find second derivative

y'' = f''(x)

Substitute all values of x

if f''(x) < 0  then x  is local maxima

if f''(x) > 0  then x  is local minima

if f''(x) = 0 then its point of inflection ( neither maxima nor minima)

y  = x² - 2

y'  = 2x

=> x = 0

y'' = 2  >0

=> x = gives minimum value for  x² - 2

y  = 2 - x²  

y'  = -2x

=> x = 0

y'' = -2 < 0

=> x = gives maximum value for  x² - 2

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