Question

evaluate each functions
$f(x) = \sqrt{5 + 6} \: find \: f(6)$
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Answer 1

Answer:

Consider a function f that is differentiable at a point x=a. Recall that the tangent line to the graph of f at a is given by the equation

y=f(a)+f^{\prime}(a)(x-a).

For example, consider the function f(x)=\frac{1}{x} at a=2. Since f is differentiable at x=2 and f^{\prime}(x)=-\frac{1}{x^2}, we see that f^{\prime}(2)=-\frac{1}{4}. Therefore, the tangent line to the graph of f at a=2 is given by the equation

y=\frac{1}{2}-\frac{1}{4}(x-2).