suppose that ( h(x)=f(x)-2g(x), f(-1)=3 ) and ( g(-1)=-2 ).\nfind ( h(-1) ).
suppose that ( h(x)=f(x)-2g(x), f(-1)=3 ) and ( g(-1)=-2 ).\nfind ( h(-1) ).
Answer
Explanation:
Step1: Differentiate ( h(x) )
According to the sum - difference rule of differentiation ((u - v)^\prime=u^\prime - v^\prime). If (h(x)=f(x)-2g(x)), then (h^\prime(x)=f^\prime(x)-2g^\prime(x)) (by the constant multiple rule ((cu)^\prime = cu^\prime) where (c = 2)).
Step2: Substitute (x=-1)
We know that (f^\prime(-1) = 3) and (g^\prime(-1)=-2). Substitute these values into the formula for (h^\prime(x)) at (x =-1). So (h^\prime(-1)=f^\prime(-1)-2g^\prime(-1)). Substitute (f^\prime(-1) = 3) and (g^\prime(-1)=-2) into the right - hand side: (h^\prime(-1)=3-2\times(-2)). First, calculate (2\times(-2)=-4). Then (h^\prime(-1)=3+4).
Answer:
(7)