Find the  equation of the tangent to the curve `y- x^2 + 4x - 5 = 0`  at the point (5,10) y-x^2+4x-5=0

Expert Answers

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

 Write the equation in standard form:

`y= x^2 - 4x+ 5 ` Use the derivative to find the gradient (multiply the power of x by the coefficient  so 2 x 1 = 2 and then minus 1 from the power so `x^2` becomes x and the same for -4x so 1x -4=-4 and the x power reduces to 0 `x^(1-1)`  :

`y' = 2x - 4` now substitute the x value in terms of the question(5;10)

 = 2(5) - 4

 = 6

As a tangent has the equation y=mx + c now substitute the x value, y value and value of m into the new equation to solve for c:

y= mx+c  

10= (6)(5) +c

10= 30 + c

-20 = c

`therefore` y=6x - 20

 

Approved by eNotes Editorial Team
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