# The line tangent to the graph of function f at the point (8,1) intersects the y-axis at y=3. How do you find f'(8)?

Write the equation of the line tangent to the graph at

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Point Slope Form solution

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To find f'(8), we can use the fact that the line tangent to the graph of function f at the point (8,1) intersects the y-axis at y=3. The slope of this tangent line is equal to the derivative of f at x=8, which is f'(8). Since the line intersects the y-axis at y=3, we know that the y-coordinate of the point (8,1) is 3 units below the y-intercept of the tangent line. Therefore, the slope of the tangent line is equal to the change in y divided by the change in x, which is (1-3)/(8-0) = -2/8 = -1/4. Hence, f'(8) = -1/4.

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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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