Question

Find the derivatives of the following functions using first principle.

f(x) = – 4x + 7

Answer 1

f(x + Δx) = – 4(x + Δx) + 7

f(x + Δx) – f(x) = [– 4(x + Δx) + 7] – [– 4x + 7]

f(x + Δx) – f(x) = [– 4(x + Δx) + 7] + 4x – 7

f(x + Δx) – f(x) = – 4 Δx

`(f(x + Deltax) - f(x))/(Deltax) = - 4 (Deltax)/(Deltax)`

`lim_(Deltax -> 0) (f(x + Deltax) - f(x))/(Deltax) = lim_(Deltax -> 0) - 4`

`f"'"(x)` = – 4