The domain of f(x)= x+sqrt(x) is all real numbers greater than or equal to 0. This is because the square root function is only defined for non-negative numbers.
The derivative of f(x)= x+sqrt(x) is 1+ 1/(2sqrt(x)). This can be found using the sum rule and the power rule for derivatives.
The derivative of a function represents the rate of change of the function at a specific point. In this case, the derivative of f(x)= x+sqrt(x) tells us how the function is changing at any given point along the curve.
Yes, the function f(x)= x+sqrt(x) is continuous. This means that there are no breaks or jumps in the graph of the function and it can be drawn without lifting the pen.
Yes, there is a point of inflection at x=0 in the graph of f(x)= x+sqrt(x). This is because the second derivative of the function changes sign at this point, indicating a change in concavity of the graph.