Find all values of x( if any ) where the tangent line to the graph of the given equation is hori

step 1 As we're looking at this, problem Y equals X minus square root of X. They give you a huge hint,

Find all values of x( if any ) where the tangent line to the...

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Key Concepts

Differentiation of Radical Functions

Differentiate radical functions by converting the radical into an expression with a fractional exponent (for example, rewriting the square root as x^(1/2)) and then applying the power rule. This procedure is essential for finding derivatives of functions that include radical terms, thereby determining the slope of their tangent lines.

Derivative

The derivative of a function represents its instantaneous rate of change with respect to its independent variable and is used to determine the slope of the tangent line at any given point. This concept is central to calculus and provides insights into the behavior and trends of functions.

Horizontal Tangent Line

A horizontal tangent line has a slope of zero, which is determined by setting the derivative of the function equal to zero. This condition helps identify points where the function's rate of change is momentarily zero, often corresponding to local extrema or critical points.

Power Rule

The power rule is a fundamental differentiation technique that states if a function is given by x raised to a power, its derivative is found by multiplying by the exponent and decreasing the exponent by one. This rule is applicable to functions involving both integer and fractional exponents, simplifying the process of differentiation.

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