Jrdan
contestada

Find and simplify the difference quotient of the form[tex]\fra\frac{f(x)-f(a)}{x-a} , x\neq a[/tex]

[tex]f(x)=3x^2+x ,a =4[/tex]

What is the difference quotient?

Respuesta :

caylus

Answer: 3x + 13

Step-by-step explanation:

[tex]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\\[/tex]

LammettHash

If [tex]f(x)=3x^2+x[/tex], then

[tex]f(4) = 3\cdot4^2+4 = 52[/tex]

so that the difference quotient is

[tex]\dfrac{f(x)-f(a)}{x-a} = \dfrac{3x^2+x-52}{x-4}[/tex]

Factorize the numerator:

[tex]3x^2+x-52 = (3x+13)(x-4)[/tex]

Then for x ≠ 4, we have

[tex]\dfrac{f(x)-f(a)}{x-a} = \dfrac{(3x+13)(x-4)}{x-4} = 3x+13[/tex]

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