Question

Need help with this....

Answer 1

`\boxed{(f(a+h)-f(a))/(h)=-3a^2-3ah-h^2}`

Explanation:

`f(x)=-x^3+2\\\\(f(a+h)-f(a))/(h)\\\\f(a+h)\to\text{substitute x = a + h}\\f(a)\to\text{substitute x = a}\\\\(f(a+h)-f(a))/(h)=(-(a+h)^3+2-(-a^3+2))/(h)\\\\\text{use}\ (x+y)^3=x^3+3x^2y+3xy^2+y^3\\\\=(-(a^3+3a^2h+3ah^2+h^3)+2-(-a^3)-2)/(h)\\\\=(-a^3-3a^2h-3ah^2-h^3+2+a^3-2)/(h)\\\\\text{combine like terms}`

`=((-a^3+a^3)-3a^2h-3ah^2-h^3+(2-2))/(h)\\\\=(-3a^2h-3ah^2-h^3)/(h)\\\\=(h(-3a^2-3ah-h^2))/(h)\\\\=-3a^2-3ah-h^2`