# How do you find the slope of a tangent line to the graph of the function #f(x)=x^3-2x+1# at (-1,2)?

so for,

so to find the gradient of the tangent we sub in the x value of the point.

The gradient of the tangent is 1 at the point (-1,2)

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To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function. The derivative of f(x) is f'(x), which represents the rate of change of the function at any given point. To find the slope of the tangent line at (-1,2), you need to evaluate the derivative at x = -1.

The derivative of f(x) = x^3 - 2x + 1 is f'(x) = 3x^2 - 2.

Substituting x = -1 into the derivative, we get f'(-1) = 3(-1)^2 - 2 = 3 - 2 = 1.

Therefore, the slope of the tangent line to the graph of f(x) = x^3 - 2x + 1 at (-1,2) is 1.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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