Suppose that a function f(125)=52 and f'(125)=4. Estimate f(123.5)

Answer 1

If f(x0)=y0, and f'(x0)=y', then an approximation to f(x0+h)=f(x0)+h*y'
Thus,
x0=125,
h=-1.5
f(x0)=52
y'=4

f(123.5)
=f(125-1.5)
=f(125)+(-1.5)(4)
=52-1.5*4
=46 (approx.)