Question

Suppose f (x) = | x – 1 | + a if x £ 1 = 2x + 3 if x > 1

if f (x) has a local minimum at x = 1, then which of the following is most appropriate –

• A. a £ 5
• B. a ³ 5
• C. a £ 0
• D. a ³ 0

Answer 1

Answer: (A)

a £ 5

Answer 2

f(x) = |x –1| + a x £ 1

= 2x + 3 x > 1

f(1 + h) > f (1)

f (1 – h) > f (1)

f(1) = a ̃ 2 (1 + h) + 3 > a ̃ a < 5