examine the maxima and minima of the function f(x)=2x³-21x²+36x-20. Also find the maximum and minimum value of f(x)
Answers
2) write f'(x)=0 and find two value of x
3) now diff. It again mean find f"(x)
4) put value of x (both value) in f"(x)
5) if u find negative sign value put in f(x) first eq. Andit will be ur maximum value
6) if u find positive value put in same eq f(x) , it will be your minimum value
Minimum Vale = -128 at x = 6 & Maximum Value = -3 at x = 1 for f(x) = 2x³ - 21x² + 36x - 20
Step-by-step explanation:
f(x) = 2x³ - 21x² + 36x - 20
f'(x) = 6x² - 42x + 36
put f'(x) = 0
=> 6x² - 42x + 36 = 0
=> x² - 7x + 6 = 0
=> x² - 6x - x + 6 = 0
=> x(x - 6) - 1(x - 6) =0
=> (x - 1)(x - 6) = 0
x = 1 or x = 6
f''(x) = 12x - 42
f''(1) = 12 - 42 = -30 -ve hence maxima
f(1) = 2 -21 + 36 - 20 = -3
f''(6) = 12*6 - 42 = +30 +ve hence minima
f(6) = 2(216) -21(36) + 36(6) - 20 = -128
Minimum Vale = -128 at x = 6
Maximum Value = -3 at x = 1
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