Answer:
a)(x+h+2)²=x²+2xh+h²+4x+4h+2
b)(x+h+2)²–(x+2)²=2xh+h²+4h
c)2x+4+h
Step-by-step explanation:
f(x)=x²+4x+2
Aight so for part a you have to replace x with x+h
a)f(x+h)=(x+h)²+4(x+h)+2=x²+2xh+h²+4x+4h+2
and then for part b you need to subtract f(x) from part a:
b)f(x+h)–f(x)=x²+2xh+h²+4x+4h+2–x²–4x–2===>
2xh+h²+4h
and for part c divide the answer by h:
c)
[tex] \frac{f(x + h) - f(x)}{h} = = = > \\ \frac{2xh + 4h + {h}^{2} }{h} = = = > \\ 2x + 4 + h[/tex]
and if you limit h by 0 you'll get the derivative of f(x)
