How do you find the gradient of the tangent to the curve #y=x^3# at the given value of x=4?

Answer 1
You start by evaluating the derivative #y'# of the function and then substitute #x=4# in it:
#y'(x)=3x^2#
substitute #x=4#;
#y'(4)=3*4^2=48# which is your gradient.
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Answer 2

To find the gradient of the tangent to the curve y=x^3 at x=4, we need to find the derivative of the function y=x^3 and evaluate it at x=4. The derivative of y=x^3 is given by dy/dx = 3x^2. Evaluating this at x=4, we get dy/dx = 3(4)^2 = 48. Therefore, the gradient of the tangent to the curve y=x^3 at x=4 is 48.

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Answer from HIX Tutor

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.

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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