How do you find the equation of the tangent line at x=3 for the function #y=2x^2-8x+7#?

1 Answer
Jim G.
Dec 13, 2016

#y=4x-11#

Explanation:

The equation of the tangent in #color(blue)"point-slope form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the gradient and # (x_1,y_1)" a point on the tangent"#

#"At x= a, the gradient of the tangent is " dy/dx#

#rArrdy/dx=4x-8#

#"at x = 3 " dy/dx=12-8=4#

#"and " y=18-24+7=1rArr(3,1)" is point on tangent"#

#rArry-1=4(x-3)rArry-1=4x-12#

#rArry=4x-11" is the equation of the tangent"#

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