For y = f(x) = 5x - 8, x = 5, and $$\Delta x = 2$$ find a) $$\Delta y$$ for the given x and $$\Delta x$$ values, b) dy = f '(x)dx, c) dy for the given x and $$\Delta x$$ values.
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The function is $$y = f(x) = 5x - 8$$. Given $$x = 5$$ and $$\Delta x = 2$$. $$\Delta y = f(x + \Delta x) - f(x)$$ First, calculate $$f(x)$$: $$f(5) = 5(5) - 8 = 25 - 8 = 17$$ Next, calculate $$f(x + \Delta x)$$: $$x + \Delta x = 5 + 2 = 7$$ $$f(7) = 5(7) - 8 = 35 Show more…
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