Find the slopes of the tangent lines to the curve y=x^2-1 at the points where x=-2,-1,0,1,2 (see

step 1 The big idea in this problem is what the tangent slope is by definition. So what I've written in

Find the slopes of the tangent lines to the curve y=x^2-1 at...

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Key Concepts

Polynomial Functions

Polynomial functions are expressions composed of variables raised to non-negative integer powers, multiplied by coefficients, and summed together. They are smooth and continuous, meaning their derivatives exist at all points, making them an excellent subject for applying differentiation techniques to find tangent slopes.

Differentiation

Differentiation is the process of computing the derivative of a function. It involves applying rules such as the power rule, product rule, and chain rule to determine how a function changes, which in turn allows one to find the slopes of tangent lines to its graph.

Tangent Line

A tangent line to a curve at a specific point is a straight line that touches the curve at that point without crossing it nearby. The slope of this line is equal to the derivative of the function at that point, providing a linear approximation of the function's behavior in the vicinity of the point.

Derivative

A derivative represents the instantaneous rate of change of a function with respect to its independent variable. It is found using the limit process and provides the slope of the tangent line to the function at any given point, making it an essential tool in understanding how functions evolve.

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