Question

determine the max and min values of the function f

f (x) = 2x^3 - 21x^2 + 36x - 20

Answer 1

Hey!!!

Hope this answer will help u..

Answer 2

Answer:

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