Question

Consider the function f(x)-5x -x-3 and complete parts (a) through (d) (a) Find fix + h) (b) Find fkth) fs) (c) Use the above answer and the limit definition of the derivative to find the derivative of the function f (d) Find the value of the derivative of f when x-1 (a) fx+h)- Simplify your answer. Do not factor) fx+ h) fx) Simplify your answer Do not factor.) c) f(x) E (d) The derviative f(1) elfo Simplify your answer)

Answer 1

f (x) = 5x^2 - x - 3 f 9 x + h) = 5 (x + h)^2 - (x + h) - 3 = 5 (x62 + 2xh + h62) - (x + h) - 3 = 5x^2 - x + 10 hx + 5h^2 - h - 3 f (x + h) = 5x62 - x + 10 hx + 5h^2 - h - 3. f (x + h) - f (x)/h = 5x62 - x + 10 hx + 5h^52 - h - 3 - 5x^2 + x + 3/h = 10hx + 5h^2 - h/h = h (10 x + 5h - 1)/h f (x + h) - f (x)/h = 10 x + 5h - 1. f^1 (x) = lim_h rightarrow 0 f (x + h) - f (x 0/h = Lim_h rightarrow 0 (10 x + 5h - 1 0 = 10 x - 1 f^1 (1) = 10 - 1 = 9 f^1 (1) = 9.