Let f(x)=−4x^(3)+6.5x+2.
1. First choose the interval of length .1 with -2 being the left endpoint of the interval. Then f′(−2)
2. Now let the interval have length .01. Then f′(−2)≈
3. Finally let the interval have length .001 Then f′(−2)
AAAaannndd the bot gets it wrong yet again!
The question is poorly worded. They want approximations for f'(-2).
That would be
(f(-2+h)-f(-2))/h
So they want
with h=0.1, f'(-2) ≈ -39.14
with h=0.01, f'(-2) ≈ -41.260
with h=0.001, f'(-2) ≈ -41.476
true value of f'(-2) = -41.5
≈
1. f'(-2) = -12x^2 + 6.5 = -11.5
2. f'(-2) ≈ -11.99
3. f'(-2) ≈ -11.995