$$f(x+\Delta x)-f(x) = \Delta y \approx dy.\]
$$f(x+\Delta x)-f(x) = \Delta y \approx dy$$
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$$f(4.5)-f(4) = \Delta y \approx dy = f'(4)\cdot dx = 1/4 \cdot 1/2 = 1/8 = 0.125.\]
$$f(4.5)-f(4) = \Delta y \approx dy = f’(4)\cdot dx = 1/4 \cdot 1/2 = 1/8 = 0.125$$
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$$f(c+\Delta x) \approx \ell(c+\Delta x),\]
$$f(c+\Delta x) \approx \ell(c+\Delta x)$$
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$$ \ell(x) = \frac12(x-\pi/3)+0.866.\]
$$\ell(x) = \frac12(x-\pi/3)+0.866$$
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$$y = f'(c)(x-c)+f(c).\]
$$y = f’(c)(x-c)+f(c)$$
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