Answer:
(a) 2(x -a)
(b) 4x +2h
Step-by-step explanation:
Fill in the function arguments and simplify.
a.
[tex]\dfrac{f(x)-f(a)}{x-a}=\dfrac{(2x^2-7)-(2a^2-7)}{x-a}\\\\=\dfrac{2x^2-7-2a^2+7}{x-a}=\dfrac{2(x^2-a^2)}{x-a}\\\\=\dfrac{2(x-a)(x+a)}{(x-a)}=2(x+a)[/tex]
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b.
[tex]\dfrac{f(x+h)-f(x)}{h}=\dfrac{(2(x+h)^2-7)-(2x^2-7)}{h}\\\\=\dfrac{2x^2+4xh+2h^2-7-2x^2+7}{h}=\dfrac{4xh+2h^2}{h}\\\\=4x+2h[/tex]
