Precalc FInd the difference quotient

Question

Find f(a), f(a + h), and the difference quotient f(a+h)- f(a)/h, where h =0.

f(x) = 7x² + 3

f(a) =

f(a + h) =

f(a+h) - f(a)/h =

Answer 1

f(a)=

𝑓(𝑥) = 7x² + 3

Plug in "a" for "x"

𝑓(𝑥) = 7a² + 3

f(a+h)=

𝑓(𝑥) = 7x² + 3

Plug in "a+h" for "x"

𝑓(𝑥) = 7(a+h)² + 3

f(a+h) - f(a)/h =

We have "f(a+h)" as well as "f(a)" already

We must substitute what we have from the first 2 steps, into the new equation

7(a+h)² + 3 - (7a² + 3) / h

Find common denominator, of "h". This means taking the left term and multiplying it by "h/h"

[7(a+h)² + 3]h /h. - (7a² + 3)/ h

Then...

common denominators, we can subtract numerators

{ 7(a+h)² + 3-(7a² + 3) } / {h}

Simplify the numerator

{ 7(a²+2ah+h²) +3 - 7a² -3 } / {h}

{7a²+14ah+7h²+3 -7a²-3} / {h}

14ah+7h² / h

h(14a+7h) / h

=14a+7h

Answer 2

f(x) = 7x² + 3

[f(a+h) - f(a)] / h = [7(a+h)² + 3 - (7a² + 3)] / h = [7(a² + 2ah + h²) - 7a²] / h = (14ah + 7h²) / h =

h(14a + 7h) / h = 14a + 7h