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categoryرياضيات schoolبكالوريوس event_available2026-07-15

السؤال

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Let f be a twice-differentiable function with f(1.5)=3. The derivative of f is given by f'(x) = (7x-19) sin(x² - 4x+4) for 1≤x≤4 (b) Use the line tangent to the graph of ƒ at x = 1.5 to approximate f (1.8). On the interval 1.5≤1.8, f'(x) < 0 and f" () > 0. Is the approximation found in part (b) an overestimate or an underestimate for f (1.8)? Give a reason for your answer. Using the Mean Value Theorem, explain why the average rate of change of f over the interval 1≤x≤4 cannot equal 6.5.

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