33a 2 Forthe functionis defined by On which two intervals is

3-3a #2

Forthe functionis defined by On which two intervals is the function increasing (enter intervals in ascending order)? to and to Find the region in which the function is positive:to Where does the function achieve its minimum?

Solution

considering f\'(x) = 0 , we get the critical values of f
critical values of f are x = -15 , - 7/13 , -1 , 0 and 10

f(-15) = - (15)⁷(16)⁶

f(-1) = 0

f(-7/13) = - (7)⁷(6)⁶ / 13¹³

f(0) = 0

f(10) = 10⁷(11)⁶

f(x) is increasing in the intervals (-15 , -1) and (-7/13 , 10)

f(x) is positive in the region (0,10)

f(x) i minimum at x=15 and attains local minimum at x= -7/13