Let f be the function defined by f(x) = 3 / (2x^2 - 7x + 5). (a) Find the slope of the line tangent to the graph of f at x = 3. (b) Find the x-coordinate of each critical point of f in the interval 1 < x < 2.5. Classify each critical point as the location of a relative minimum, a relative maximum, or neither. Justify your answers.
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The derivative of \( f \) is given by: \( f'(x) = -\frac{6x-7}{(2x^2-7x+5)^2} \) Evaluating \( f'(x) \) at \( x = 3 \) gives: \( f'(3) = -\frac{6(3)-7}{(2(3)^2-7(3)+5)^2} = -\frac{11}{16} \) So, the slope of the tangent line to the graph of \( f \) at \( x = Show more…
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