simplify-the-difference-quotient-fxfaxafracfleftxright-fleftarightx-a-for-the-fu

Question

Simplify the difference quotient f(x)−f(a)x−a\frac{f\left(x\right)-f\left(a\right)}{x-a} for the function f(x)=2x3−1xf\left(x\right)=$$2x^3$$-\frac{1}{x}.

Accepted Answer

f(x)−f(a)x−a=2ax(x2+ax+a2)+1ax\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2ax\$$left(x^2$+ax+a^2$$\right)+1}{ax}

Answer

f(x)−f(a)x−a=2ax(x3−3a2x−3ax2+a3)+1ax\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2ax\$$left(x^3-3a^2$x-3ax^2$+a^3$$\right)+1}{ax}

Answer

f(x)−f(a)x−a=2ax(x3+3a2x+3ax2+a3)+1ax\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2ax\$$left(x^3+3a^2$x+3ax^2$+a^3$$\right)+1}{ax}

Answer

f(x)−f(a)x−a=2ax(x2+x+a2)+1ax\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2ax\$$left(x^2$+x+a^2$$\right)+1}{ax}

Simplify the difference quotient f(x)−f(a)x−a\(\frac{f\left(x\right)-f\left(a\right)}{x-a}\) for the function f(x)=2x3−1xf\(\left\)(x\(\right\))=2x^3-\(\frac{1}{x}\).

Simplify the difference quotient $\frac{f (x) - f (a)}{x - a}$ for the function $f (x) = 2 x^{3} - \frac{1}{x}$ .