# How do you find the horizontal tangent of #y= (4x^2-2) / (x^2)#?

The horizontal tangent is

To look for the horizontal tangent, you look the limit of y as x tends to plus or minus infinity.

You take the highest coefficient of the numerator,

graph{(y-(4x^2-2)/x^2)(y-4)=0 [-7.9, 7.906, -1.886, 6.016]}

By signing up, you agree to our Terms of Service and Privacy Policy

To find the horizontal tangent of the function y = (4x^2-2) / (x^2), we need to determine the values of x where the derivative of the function is equal to zero.

First, we find the derivative of the function using the quotient rule:

y' = [(2x^2)(8x) - (4x^2-2)(2x)] / (x^2)^2

Simplifying this expression, we get:

y' = (16x^3 - 4x^4 + 4x) / x^4

Next, we set the derivative equal to zero and solve for x:

(16x^3 - 4x^4 + 4x) / x^4 = 0

Multiplying both sides by x^4, we have:

16x^3 - 4x^4 + 4x = 0

Factoring out x, we get:

x(16x^2 - 4x^3 + 4) = 0

Setting each factor equal to zero, we have two possibilities:

x = 0 or 16x^2 - 4x^3 + 4 = 0

Solving the quadratic equation 16x^2 - 4x^3 + 4 = 0 may require the use of numerical methods or a graphing calculator.

Therefore, the horizontal tangent of the function y = (4x^2-2) / (x^2) occurs at the x-values obtained from solving the equation 16x^2 - 4x^3 + 4 = 0.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- Let #f(x)=(5/2)sqrt(x)#. The rate of change of f at #x=c# is twice its rate of change at #x=3#. What is the value of c?
- How do you find the average rate of change for the function #s(t)=4.5t^2# on the indicated intervals [6,12]?
- What is the equation of the line normal to #f(x)=4x^2-7x+6 # at #x=1#?
- How can instantaneous velocity be found from a displacement-time graph?
- What is the equation of the normal line of #f(x)=-x^4+4x^3-x^2+5x-6# at #x=2#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7