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## Homework Statement

hey Forum! I had a question here I'm struggling with and was wondering if someone could take a look. its Dealing with calculus, specifically derivatives and behaviors of the graph:

http://i41.tinypic.com/mc6opj.jpg

I just started and part a) already has me stumped D:

## The Attempt at a Solution

for intervals of increase or decrease I know we must equate the first derivative to zero.

f(x) = x^3 – x^2 + 4x – 3

f’(x) = 3x^2 – 2x + 4

f’’(x) = 6x – 2

so:

f’(x) = 3x^2 – 2x + 4

0 = 3x^2 – 2x + 4

however I couldn't factor this.. and when I tried to use the quadratic formula.. I got a negative discriminant.

From what I gather this means the derivative has no real roots.. However the actual graph of the original function crosses the x axis just before 1.. I'm confused! how do I calculate this?

any advice would be wicked!