Find an equation of the tangent line to the graph of  y = g(x) at x = 6 if g(6) = −3 and g'(6) = 2.  

Expert Answers

An illustration of the letter 'A' in a speech bubbles

You need to remember the form of equation of tangent line to the graph of function at a point `x=a`  such that:

`g(x)- g(a) = g'(a)(x-a)`

Notice that the problem does not provide the equation of function, but it provides the values of `g(x) ` and `g'(x)`  at `x =6`  such that:

`g(x) - g(6) = g'(6)(x-6)`

Substituting -3 for `g(6)`  and 2 for `g'(6)`  yields:

`g(x) -(-3) = 2(x-6) => g(x) + 3 = 2x - 12`

Substituting y for g(x) yields:

`y = 2x - 12 - 3 => y = 2x - 15`

Hence, evaluating the equation of the tangent line to the graph of the function g(x), at x = 6, yields `y = 2x - 15.`

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial