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.
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 line normal to # f(x)=sqrt(e^(sqrtx)# at # x=4#?
- What is the instantaneous velocity of an object with position at time t equal to # f(t)= (t^2-8,tsqrt(t^2+3t-4)) # at # t=2 #?
- What is Rate of Change of a Function?
- What is the slope of the line normal to the tangent line of #f(x) = e^-x+x^2-x # at # x= 0 #?
- How do you find the slope of the curve #f(x)=sqrt(x-1)# at the point x=5?

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