Question

Find and simplify the difference quotient of the forma%7D%20%2C%20x%5Cneq%20a" id="TexFormula1" title="\fra\frac{f(x)-f(a)}{x-a} , x\neq a" alt="\fra\frac{f(x)-f(a)}{x-a} , x\neq a" align="absmiddle" class="latex-formula">
$f(x)=3x^2+x ,a =4$

What is the difference quotient?

Answer 1

If $f(x)=3x^2+x$, then

$f(4) = 3\cdot4^2+4 = 52$

so that the difference quotient is

$\dfrac{f(x)-f(a)}{x-a} = \dfrac{3x^2+x-52}{x-4}$

Factorize the numerator:

$3x^2+x-52 = (3x+13)(x-4)$

Then for x ≠ 4, we have

$\dfrac{f(x)-f(a)}{x-a} = \dfrac{(3x+13)(x-4)}{x-4} = 3x+13$

Answer 2

Answer: 3x + 13

Step-by-step explanation:

$f(x)=3x^2+x\\f(a)=3a^2+a\\f(4)=3*4^2+4=52\\\\f(x)-f(4)=3x^2+x-52=(x-4)(3x+13)\\\\\dfrac{f(x)-f(4)}{x-4} =\dfrac{3x^2+x-52}{x-4} \\\\if\ x \neq 4\ then \\\\\dfrac{f(x)-f(4)}{x-4} =\dfrac{(x-4)(3x+13)}{x-4} \\\\=3x+13$