Estimation Instantaneous rate of change

Question

Estimate the instantaneous rate of change of the function f(x) = xlnx at x = 18 and x = 19.

f'(18) ≈

f'(19)

Answer 1

The instantaneous rate of change at a point is the derivative at that point.

d/dx xlnx =d/dx of x * lnx + d/dx of lnx * x

d/dx of x = 1

d/dx of lnx = 1/x

d/dx of xlnx = 1*lnx + 1/x * x = lnx + 1 = f'(x)

f'(18) = ln(18)+1 = about 3.89

f'(19) = ln(19) + 1 = about 3.94