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(D) Given the function $f(x) = x^{3} + 5x^{2} - 7x + 10$.First,find the derivative $f'(x) = 3x^{2} + 10x - 7$.Let $a = 1$ and $h = 0.1$,so $x = a + h

Vedclass · Accepted Answer

$9$

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(D) Given the function $f(x) = x^{3} + 5x^{2} - 7x + 10$.First,find the derivative $f'(x) = 3x^{2} + 10x - 7$.Let $a = 1$ and $h = 0.1$,so $x = a + h = 1.1$.Calculate $f(a) = f(1) = (1)^{3} + 5(1)^{2} - 7(1) + 10 = 1 + 5 - 7 + 10 = 9$.Calculate $f'(a) = f'(1) = 3(1)^{2} + 10(1) - 7 = 3 + 10 - 7 = 6$.Using the linear approximation formula $f(a + h) \approx f(a) + h \cdot f'(a)$:$f(1.1) \approx 9 + (0.1)(6) = 9 + 0.6 = 9.6$.

The approximate value of the function $f(x) = x^{3} + 5x^{2} - 7x + 10$ at $x = 1.1$ is (in $.6$)

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