# How do you find the slope of the tangent to the curve #y = 3 + 4x^2 - 2x^3# where x = a?

The derivative of a function is the slope of the tangent to that function.

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To find the slope of the tangent to the curve y = 3 + 4x^2 - 2x^3 at x = a, you need to find the derivative of the function y with respect to x, then evaluate it at x = a. The derivative of the function y = 3 + 4x^2 - 2x^3 is given by:

dy/dx = d/dx(3 + 4x^2 - 2x^3)

dy/dx = 0 + 8x - 6x^2

Now, to find the slope of the tangent at x = a, substitute a for x in the derivative:

Slope = dy/dx at x = a = 8a - 6a^2

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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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