How do you find the equation of the tangent line to the graph of the given function #f(x) =  1/x#; at (3,1/3)?
I found:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the equation of the tangent line to the graph of the function f(x) = 1/x at the point (3, 1/3), we can follow these steps:

Find the derivative of the function f(x) using the quotient rule. The derivative of f(x) = 1/x is f'(x) = 1/x^2.

Substitute the xcoordinate of the given point (3, 1/3) into the derivative to find the slope of the tangent line. f'(3) = 1/3^2 = 1/9.

Use the pointslope form of a linear equation, y  y1 = m(x  x1), where (x1, y1) is the given point and m is the slope, to write the equation of the tangent line. Plugging in the values, we get y  (1/3) = (1/9)(x  3).

Simplify the equation to obtain the final form of the tangent line. The equation of the tangent line to the graph of f(x) = 1/x at (3, 1/3) is y + 1/3 = (1/9)(x  3).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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 slope of #f(x)=e^(x3x^3) # at #x=2#?
 How do you find f'(x) using the definition of a derivative for #f(x)= 1/(x3)#?
 How do you use the definition of a derivative to find the derivative of #f(x)=4+x2x^2#?
 How do you find the slope of the tangent line to the graph of the function #f(x)=5x^2# at (2,1)?
 How do you find the equation of a line tangent to the function #y=2x^25x# at (2,2)?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7