Let f(x)=2^1.4x. Estimate the derivative f′(1.1) to within two decimal places by using a small enough interval
AAAaannndd the bot gets it wrong yet again!
to get an estimate, use
f'(1.1) ≈ (f(1.1+h)-f(1.1))/h = (2^(1.4(1.1+h)) - 2^(1.4*1.1))/h
h f'(1.1)
0.1 2.96
0.05 2.89
0.01 2.84
0.001 2.823
f'(1.1) = 1.4 ln2 2^1.54 = 2.82189