Question

Use linear approximation to approximate f(0.8) given f(x)=2x^3-3x+1

I'm not sure how to do it without a point given.

Answer 1

f(1) = 2-3+1 = 0
df = (6x^2-3) dx
So, starting from f(1),
f(0.8) = f(1)+(6-3)(-0.2) = -1.8

The line is
y-0 = 3(x-1)

You can see the approximation at

http://www.wolframalpha.com/input/?i=plot+2x^3-3x%2B1%2C3%28x-1%29

You could have started with a different value of x, say, x=0.9, and used a smaller dx, but x=1 is convenient and moderately close.