×
Back to all chapters

# Higher-order Derivatives

The first derivative is the slope of a curve, and the second derivative is the slope of the slope, like acceleration. So what's the third derivative? (Fun fact: it's actually called jerk.)

# Graphical Interpretation of Higher Order Derivatives

In the above diagram, the red curve is the graph of a function $$f,$$ and the blue curve is the graph of its first derivative $$f'.$$ What is the relationship between $$f'(-1)$$ and $$f''(1) ?$$

Given the graph of $$y=f''(x)$$ above, which of the following is a possible graph of $$y=f(x)?$$

Graphs

Given the graph of $$y=f(x)$$ above, which of the following is a possible graph of $$y=f''(x)?$$

Choice4

Given the graph of $$y=f(x)$$ above, which of the following is a possible graph of $$y=f''(x)?$$

SecondDr

Given the graph of $$y=f(x)$$ above, which of the following is a possible graph of $$y=f''(x)?$$

SecondDerivatives

×