Question

How do you use the definition of a derivative to find the derivative of `f(x) = 1.5x^2 - x + 3.7`?

Answer 1

`f'(x)=lim` `h->0 ([1.5(a+h)^2-(a+h)+3.7]-[1.5a^2-a+3.7])/h = (1.5(a^2+2ah+h^2)-a-h+3.7-1.5a^2+a-3.7)/h`
`=(1.5a^2+3ah+1.5h^2-a-h+3.7-1.5a^2+a-3.7)/h=(3ah+1.5h^2-h)/h =3a+1.5h-1=3a-1`

Explanation:

Find f(a+h) and f(a) and then substitute it into the definition and simplify.