Answer:
m = 12
Step-by-step explanation:
For f(x) = 2x² you want to find the slope m using ...
m = (f(x+h) -f(x))/h
at x=3.
Filling in the function definition and its arguments, we have ...
m = (2(x+h)² -2x²)/h = (2x² +4hx +2h² -2x²)/h = 4x +2h
The value of this as h goes to zero is ...
m = 4x
At x=3, the slope is ...
m = 4·3 = 12
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The attached graph shows a numerical estimate of the slope (f'(3)=12) and the line with that slope through the point P(3, 18). The line certainly appears to be tangent to the curve at that point.
