# How do you show that the curve #6x^3+5x-3# has no tangent line with slope 4?

Find the derivative. Set it equal to

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To show that the curve 6x^3+5x-3 has no tangent line with slope 4, we can find the derivative of the curve and set it equal to 4. If there are no solutions to this equation, it means there is no tangent line with slope 4. The derivative of the curve is 18x^2 + 5. Setting this equal to 4, we get 18x^2 + 5 = 4. Solving this equation, we find that there are no real solutions for x. Therefore, the curve 6x^3+5x-3 has no tangent line with slope 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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