Question

Find function then simplify tje answer

Answer 1

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

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)

`(f(x + h) - f(x))/(h) = = = > \\ \frac{2xh + 4h + {h}^(2) }{h} = = = > \\ 2x + 4 + h`

and if you limit h by 0 you'll get the derivative of f(x)