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For part c)
1 For f(x)= ax^3+bx^2+cx+d to have a local minimum (which is a stationary point) at x=-1, its derivative at that point must be equal to 0
3 its derivative f'(x) is 3ax^2+2bx+c
4 Setting this equal to 0 and substituting x=-1 into it, we get
5 3a-2b+c=0
6 If f"(k)>0, f has a local minimum value at x=k
7 f"(x)=6ax+2b
8 Setting this greater than 0 and substituting x=-1, we get
9 -6a+2b>0
10 b>3a
11 We know that b>3a , so we can substitute, say b=4a into line 5
12 Substituting, we get
13 3a-8a+c=0
14 c=5a
15 We now have ur constraints for a suitable function that meets the 16requirements
17 for example, (x^3)+4(x^2)+5x+5