Let c be a fixed number and consider the function f(x) = x - 2x^3.

Question

Let c be a fixed number and consider the function f(x) = x - 2x^3.

simplify the difference quotient f(c+h)−f(c)/h

until its deniminator is 1.

for all h doesn't equal 0,

f(c+h)−f(c)/h = _________

Answer 1

(f(c+h)-f(c))/h = (c+h-2(c+h)³-(c-2c³))/h

= (c+h-2c³-6c²h-6ch²-h³-c+2c³)/h

= (h-6c²h-6ch²-h³)/h

= (1-6c²-6ch-h²)/1