How do you find the points where the graph of the function #y=2x^3# has horizontal tangents and what is the equation?

Answer 1

#y=0#

Given -

#y=2x^3#

It is a cubic function.

It has no constant terms. Hence it passes through the origin.

The slope of a horizontal tangent is #0#

We have to find for which value of #x# the slope of the curve becomes zero.

The first derivative of the function gives the slope of the curve at any given point on the curve.

#dy/dx=6x^2#

#dy/dx=0 => 6x^2=0#

#x=0#

When #x# takes the value #0# the slope of the curve is zero.

The tangent is through #(0,0)#

Hence the equation of the tangent is #y=0#

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Answer 2

To find the points where the graph of the function y=2x^3 has horizontal tangents, we need to find the values of x where the derivative of the function is equal to zero.

First, we find the derivative of the function y=2x^3. Taking the derivative, we get dy/dx = 6x^2.

Next, we set the derivative equal to zero and solve for x: 6x^2 = 0.

Solving this equation, we find that x = 0.

Therefore, the graph of the function y=2x^3 has horizontal tangents at the point (0,0).

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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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