# How do you find the points where the graph of the function #y = x - (x / 18)^2# has horizontal tangents and what is the equation?

First, we can simplify the function.

We can find the derivative of this through the power rule:

Graphed are the tangent line and original function:

graph{(x-(x/18)^2-y)(y-81+0x)=0 [-119.8, 488.8, -146.2, 158]}

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

To find the points where the graph of the function y = x - (x / 18)^2 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 = x - (x / 18)^2 with respect to x.

The derivative is given by: dy/dx = 1 - (2x / 18^2)

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

1 - (2x / 18^2) = 0

Simplifying the equation, we have:

1 - (2x / 324) = 0

Multiplying both sides by 324, we get:

324 - 2x = 0

Solving for x, we find:

x = 162

Therefore, the point where the graph of the function has a horizontal tangent is (162, y), where y is the corresponding value of y when x = 162.

The equation of the horizontal tangent line is y = x - (x / 18)^2, evaluated at x = 162.

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 equation of the normal line of #f(x)=x^3e^-x+x^3# at #x=-5#?
- How do you find the slope of a tangent line to the graph of the function #f(x) = 8 sqrt(-3x - 1)# at x=-3?
- What is the equation of the tangent line of # f(x)=sinpix # at # x=3 #?
- A rectangle's base remains 0.5 cm while its height changes at a rate of 1.5 cm/min. At what rate is the area changing, in cm when the height is 1.5 cm?
- What is the equation of the tangent line of #f(x)=sqrt(x+1) # at #x=0#?

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