Answer:
- (a) 40; (b) -8; (c) -5
- -2/((x -1)(x -1 -h))
Step-by-step explanation:
1)
All of the values in parentheses are less than 6, so you only need the first part of the function definition.
f(x) = x^2 +6x = (x +6)x
f(4) = (4+6)(4) = 40
f(-2) = (-2 +6)(-2) = -8
f(-1) = (-1 +6)(-1) = -5
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2)
[tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{\dfrac{2}{(x+h)-1}-\dfrac{2}{x-1}}{h}=2\dfrac{(x-1)-(x+h-1)}{h(x-1)(x+h-1)}\\\\=\boxed{\dfrac{-2}{(x-1)(x-1+h)}}[/tex]
