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
_____
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.
Answer:
40 14/25 years
Step-by-step explanation:
Well, this certainly is fun.
First, to find the fraction of the doctor's life which 13 years represents, subtract the fractions from 1 (and in this case l stands for lifetime):
So, multiply this equation by the reciprocal of 25/78 to isolate one of l:
years