The difference quotient for f(x) = 3x2 – 12 is 6x + 3h
How to determine the difference quotient?
The function is given as:
f(x) = 3x^2 – 12.
Calculate f(x + h)
f(x + h) = 3(x + h)^2 – 12
The difference quotient is then calculated using:
[tex]f'(x) = \frac{f(x + h) - f(x)}{h}[/tex]
This gives
[tex]f'(x) = \frac{3(x + h)^2 - 12 - 3x^2 + 12}{h}[/tex]
Evaluate the difference
[tex]f'(x) = \frac{3(x + h)^2- 3x^2}{h}[/tex]
Expand
[tex]f'(x) = \frac{3x^2 + 6xh + 3h^2- 3x^2}{h}[/tex]
Evaluate the difference
[tex]f'(x) = \frac{6xh + 3h^2}{h}[/tex]
Evaluate the quotient
f'(x) = 6x + 3h
Hence, the difference quotient for f(x) = 3x2 – 12 is 6x + 3h
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