# How do you find the equation of a line tangent to #y=4/x# at (2,2)?

We know that the tangent passes through the point

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

To find the equation of a line tangent to the curve y = 4/x at the point (2,2), we can use the concept of differentiation.

First, we need to find the derivative of the function y = 4/x. The derivative of 4/x can be found using the power rule of differentiation, which states that the derivative of x^n is n*x^(n-1). Applying this rule, we get:

dy/dx = d(4/x)/dx = -4/x^2

Now, we can find the slope of the tangent line at the point (2,2) by substituting x = 2 into the derivative:

m = dy/dx = -4/(2^2) = -1

The slope of the tangent line is -1.

Next, we can use the point-slope form of a linear equation to find the equation of the tangent line. The point-slope form is given by:

y - y1 = m(x - x1)

Substituting the values of the point (2,2) and the slope (-1), we have:

y - 2 = -1(x - 2)

Simplifying, we get:

y - 2 = -x + 2

Rearranging the equation, we obtain the equation of the tangent line:

y = -x + 4

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 line normal to # f(x)=lnx-x# at # x=2#?
- What is the equation of the tangent line of #f(x) =(e^x-x)(e^x-x^2)# at #x=4#?
- How do you find the average rate of change of #f(t)= 2t + 7# from [1,2]?
- What is the equation of the line tangent to #f(x)=(3x-1)(2x+4)# at #x=0#?
- What is the slope of the line normal to the tangent line of #f(x) = xsecx-cos(2x-pi/6) # at # x= (15pi)/8 #?

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