Answer:
a). 8(x + a)
b). 8(h + 2x)
Step-by-step explanation:
a). Given function is, f(x) = 8x²
For x = a,
f(a) = 8a²
Now substitute these values in the expression,
[tex]\frac{f(x)-f(a)}{x-a}[/tex] = [tex]\frac{8x^2-8a^2}{x-a}[/tex]
= [tex]\frac{8(x^2-a^2)}{(x-a)}[/tex]
= [tex]\frac{8(x-a)(x+a)}{(x-a)}[/tex]
= 8(x + a)
b). [tex]\frac{f(x+h)-f(x)}{h}[/tex] = [tex]\frac{8(x+h)^2-8x^2}{h}[/tex]
= [tex]\frac{8(x^2+h^2+2xh)-8x^2}{h}[/tex]
= [tex]\frac{8x^2+8h^2+16xh-8x^2}{h}[/tex]
= (8h + 16x)
= 8(h + 2x)
