Given that f(x) = 1/x - sqrt(x) + 3. Find f'(1).
We are given that f(x) = 1/x - sqrt(x) + 3. Here, f(x) represents a function. A function is a relation or expression involving one or more variables. We are able to differentiate f(x) in order to find the gradient, f'(x), at a particular point on the graph. So the purpose of this question is to find the gradient of f(x) at x=1.
In order to differentiate quadratics, we use the typical formula where y=axb and dy/dx=abxb-1. With this information we are now able to differentiate f(x). To make f(x) simpler we write, f(x) = x-1 - x1/2 + 3. Using the formula for differentiation above, we deduce that f'(x) = -x-2 - (1/2)x-1/2. To conclude, we simply substitute x=1 into our formula for f'(x) and we obtain f'(1)= -3/2.
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