`g(t) = -2cos(t) + 5, (pi,7)` Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

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hkj1385 | (Level 1) Assistant Educator

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g(t) = -2*cost + 5

slope of the curve = g'(t) = d{g(t)}/dt = 2*sint

Thus, slope at (pi,7)

g'(pi) = 2*sin(pi) =0

Thus, the curve has a tangent parallel to the x-axis(horizontal axis) at (pi,7)