# Let #f(x) = (x+2)/(x+3)#. Find the equation(s) of tangent line(s) that pass through a point (0,6)? Sketch the solution?

##
Let #f(x) = (x+2)/(x+3)# . Find the equation(s) of tangent line(s) that pass through a point (0,6)?

Let

Tangents are

graph{(25x-9y+54)(x-y+6)(y-(x+2)/(x+3))=0 [-12.58, 7.42, -3.16, 6.84]}

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

To find the equation(s) of tangent line(s) that pass through the point (0,6) on the graph of f(x) = (x+2)/(x+3), we need to find the derivative of f(x) and substitute the coordinates of the given point into the derivative equation.

The derivative of f(x) can be found using the quotient rule:

f'(x) = [(x+3)(1) - (x+2)(1)] / (x+3)^2

Simplifying this expression gives:

f'(x) = 1 / (x+3)^2

Now, substitute the coordinates of the point (0,6) into the derivative equation:

6 = 1 / (0+3)^2

Solving for the constant value gives:

6 = 1 / 9

Multiplying both sides by 9 gives:

54 = 1

This is not possible, so there is no tangent line passing through the point (0,6) on the graph of f(x) = (x+2)/(x+3).

Therefore, there are no tangent lines to sketch.

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.

- How do you find the slope of a tangent line to the graph of the function #f(x)=x^3-2x+1# at (-1,2)?
- What is the slope of #f(x)=xe^(x-x^2) # at #x=-1#?
- Using the definition of derivative, how do you prove that (cos x)' = -sin x?
- How do you find the slope of the tangent line to the graph at given point and give an equation of the tangent line #f(x)=3/2x# at (1, 3/2)?
- What is the equation of the normal line of #f(x)= e^(x^2/(x-2))# at #x = 3#?

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