Question

a Find $f'(x)$.\n\nb Show that $f'(x) > 0$ for all $x$, and explain the significance of this result.\n\nc Use technology to sketch $y = f(x)$, and check your answer to b.\n\n7 Consider the function $f(x) = 2x + \frac{8}{x}$.\n\na Show that $f'(x) = \frac{2(x+2)(x-2)}{x^2}$.\n\nb Draw the sign diagram for $f'(x)$.\n\nc Hence find intervals where $y = f(x)$ is increasing or decreasing.\nA stationary point of a function is a point where $f'(x) = 0$.\nIt could be a local maximum or local minimum, or else a\nstationary inflection.

          a Find $f'(x)$.\n\nb Show that $f'(x) > 0$ for all $x$, and explain the significance of this result.\n\nc Use technology to sketch $y = f(x)$, and check your answer to b.\n\n7 Consider the function $f(x) = 2x + \frac{8}{x}$.\n\na Show that $f'(x) = \frac{2(x+2)(x-2)}{x^2}$.\n\nb Draw the sign diagram for $f'(x)$.\n\nc Hence find intervals where $y = f(x)$ is increasing or decreasing.\nA stationary point of a function is a point where $f'(x) = 0$.\nIt could be a local maximum or local minimum, or else a\nstationary inflection.

a Find f'(x).Show that f'(x) > 0 for all x, and explain the significance of this result.Use technology to sketch y = f(x), and check your answer to b.7 Consider the function f(x) = 2x + (8)/(x).Show that f'(x) = (2(x+2)(x-2))/(x^2).Draw the sign diagram for f'(x).Hence find intervals where y = f(x) is increasing or decreasing.stationary point of a function is a point where f'(x) = 0.could be a local maximum or local minimum, or else ainflection.

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