# How do you find the points where the tangent line is horizontal given #y=16x^-1-x^2#?

To find the points at which the tangent line is horizontal, we have to find where the slope of the function is 0 because a horizontal line's slope is 0.

That's your derivative. Now set it equal to 0 and solve for x to find the x values at which the tangent line is horizontal to given function.

You can confirm this by graphing the function and checking if the tangent line at the point would be horizontal:

graph{(16x^(-1)) - (x^2) [-32.13, 23, -21.36, 6.24]}

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

To find the points where the tangent line is horizontal for the equation y = 16x^(-1) - x^2, we need to find the values of x where the derivative of y with respect to x equals zero.

First, we find the derivative of y with respect to x: dy/dx = -16x^(-2) - 2x

Next, we set the derivative equal to zero and solve for x: -16x^(-2) - 2x = 0

To simplify the equation, we multiply through by -x^2: 16 + 2x^3 = 0

Rearranging the equation, we have: 2x^3 = -16

Dividing both sides by 2, we get: x^3 = -8

Taking the cube root of both sides, we find: x = -2

Therefore, the point where the tangent line is horizontal is when x = -2.

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.

- What is the average value of the function # F(t)=Sin^3(t)cos^3(t)# on the interval #[-pi, pi]#?
- How do you use the limit definition to find the slope of the tangent line to the graph #f(x)=x^3#?
- What is the equation of the tangent line of #f(x)=Arctan(x/3) # at #x=0#?
- How do you find the average value of: #f(x) = 8 sin x + 6 cos x# on the interval #[0,(10pi)/6 ]#?
- Using the limit definition, how do you find the derivative of # f(x) = (x^2-1) / (2x-3)#?

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