1.      Let f(x) = ax3 + 6x2 +bx + 4.  Determine the constants a and b so that f has a relative minimum at x = -1 and a relative maximum at x = 2.  Show all working!

aruv | Student




Since f(x) has minimum value at x=-1. Therefore



a<2                     (i)

And f(x) has maximum value at x=2, therefore


`a<-1`                 (ii)

Thus from (i) and (ii)


Since x=-1 and x=2 are relative minima  and relative maxima, therefore




3a-12+b=0           (iii)

12a+24+b=0         (iv)

Subtract (iii) from (iv),



Substitute a=-4 in (iii), we have b=24.

Thus we have a=-4 and b=24.