Use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an

step 1 Okay, so we have the curve x squared minus 4x, and we want to know the slope of the line tangent

Use the method in Example 3 to find (a) the slope of the...

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Key Concepts

Tangent Line

A tangent line to a curve at a given point is a line that touches the curve at that point and has the same slope as the function does at that point. This line serves as the best linear approximation of the curve near the point of tangency.

Point-Slope Form

The point-slope form is a technique for writing the equation of a line when a point on the line and its slope are known. It is expressed as y - y? = m(x - x?), and it is especially useful in finding the equation of a tangent line once the slope from the derivative is determined.

Derivative

The derivative of a function is a measure of its instantaneous rate of change. It is defined as the limit of the difference quotient as the interval approaches zero, capturing how the function behaves locally and providing the slope of the tangent at any specific point on the curve.

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