# How do you use the limit definition to find the slope of the tangent line to the graph #f(t) = t − 13 t^2# at t=3?

# f'(3)=-77#

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To find the slope of the tangent line to the graph of f(t) = t - 13t^2 at t=3 using the limit definition, we can follow these steps:

- Start with the given function f(t) = t - 13t^2.
- Determine the derivative of f(t) with respect to t, denoted as f'(t), by applying the power rule and constant rule. In this case, f'(t) = 1 - 26t.
- Substitute the value t=3 into the derivative f'(t) to find the slope at that specific point. Thus, f'(3) = 1 - 26(3) = -77.
- The slope of the tangent line to the graph of f(t) at t=3 is -77.

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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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