Question

Let f(x) = x³ + 3x² – 9x + 2. Then f(x) has

A. a maximum at x = 1 

B. a minimum at x = 1 

C. neither a maximum nor a minimum at x = 3 

D. none of these

Answer 1

Option : (B)

f(x) = x³ + 3x² - 9x+2 

f’(x) = 3x² + 6x - 9 

f’(x) = 0 

3x² + 6x - 9 = 0 

By solving the quadratic we get roots as follows 

x = - 3 and x = 1 

Hence by second derivative test 

f’’(x) > 0 or f”(x) < 0 

So, 

At x = 1 minimum value.