determine the equation of the line tangent to the graph of y=9e^(3x^2)-4x at x=3 in the form y=mx+b has m= b=

Expert Answers

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

You need to remember what is the form of equation of the tangent line to the graph of the function, at the point x = 3, such that:

`y - f(3) = f'(3)(x - 3)`

You need to determine f(3) substituting 3 for x in equation of teh function such...

See
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Get 48 Hours Free Access

You need to remember what is the form of equation of the tangent line to the graph of the function, at the point x = 3, such that:

`y - f(3) = f'(3)(x - 3)`

You need to determine f(3) substituting 3 for x in equation of teh function such that:

`f(3) = 9e^(27)-12`

You need to determine f'(x) such that:

`f'(x) = 9e^(3x^2)*(3x^2)' - 4 => f'(x) = 54x*e^(3x^2)`

You need to determine f'(3) substituting 3 for x in equation of teh function such that:

`f'(3) = 54x*e^(3x^2) => f'(3) = 162*e^27`

You may write the equation of tangent line such that:

`y -9e^(27)+12 = 162*e^27(x - 3)`

You need to put the equation in slope intercept form, such that:

y = 9e^27 -12 + 162x*e^27 - 486*e^27

`y = 162x*e^27 - 477*e^27 - 12`

Hence, evaluating the equation of tangent line yields `y = 162x*e^27 - 477*e^27 - 12`  where `m = 162*e^27 ` and `b =- 477*e^27 - 12.`

Approved by eNotes Editorial Team