For the function shown below, which is greater: f'(x1) or f'(x2)?
Draw the tangent lines to f at x1andx2:
The slope of the tangent line to f at x1, also known as f'(x1), looks like about 0. The slope of the tangent line to f at x2, also known as f'(x2), looks decidedly more negative. We conclude that f'(x1) is greater.