\[ f(x)=\left\{\begin{array}{ll} \sqrt{9-x^{2}} & \text { for }-3 \leq x \leq 0 \\ -x+3 \cos \left(\frac{\pi x}{2}\right) & \text { for } 0<x \leq 4 \end{array}\right. \] 3. Let \( f \) be the function defined above. (a) Find the average rate of change of \( f \) on the interval \( -3 \leq x \leq 4 \). (b) Write an equation for the line tangent to the graph of \( f \) at \( x=3 \).
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We need to find the values of f(-3) and f(4). For x = -3, we use the first part of the piecewise function: \[ f(-3) = \sqrt{9 - (-3)^2} = \sqrt{9 - 9} = 0 \] For x = 4, we use the second part of the piecewise function: \[ f(4) = -4 + 3\cos\left(\frac{\pi \cdot Show more…
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