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## Curve Sketching

You don't need a calculator or computer to draw your graphs! Derivatives and other Calculus techniques give direct insights into the geometric behavior of curves.

# Curve Sketching Warmup

The graph of $$y = f(x)$$ is shown. On which intervals is $$f'(x) > 0?$$

The graphs of $$y = g(x)$$ and $$y = h(x)$$ are shown above. Which is the derivative of the other?

The graph of $$y = g'(x)$$ (the derivative of $$g(x)!)$$ is shown. At what value of $$x$$ does $$g(x)$$ obtain a local maximum?

On what intervals is $$f(x) = x^3 - 12x$$ increasing?

$$A = (-\infty, -2)$$

$$B = (-2, 2)$$

$$C = (2, \infty)$$

A penguin is climbing up a long slippery slope, taking occasional breaks to slide back down for a bit. The penguin's vertical height (in meters) above a fixed point at time $$t$$ minutes after starting is represented by $$f(t).$$ Based on the information about $$f'(t)$$ in the table below, at which of these times did the penguin's height reach a local minimum?

 Interval Sign of $$f'(t)$$ $$(0,1)$$ + $$(1,2)$$ - $$(2,3)$$ - $$(3,4)$$ +
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