Question

Let f(x) is a three degree polynomial for which f '(–1) = 0, f ''(1) = 0, f(–1) = 10, f(1) = 6 then local minima of f(x) exist at

(1) x = 3 

(2) x = 2 

(3) x = 1 

(4) x = –1  

Answer 1

Answer is (1) x = 3

Let f(x) = ax³ + bx² + cx + d

a = 1/4 d = 35/4

b = -3/4 c = - 9/4

⇒ f(x) = a(x³ - 3x² - 9x) + d

f'(x) = 3/4(x² - 2x - 3)

⇒ f'(x) = 0 x = 3, - 1

local minima exist at x = 3