# Find the tangent.

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• Mar 28th 2006, 11:22 PM
classicstrings
Find the tangent.
How would i find the tangent to the quadratic 2x^2 -12x + 14 at the point (1,4)? Do we take the derivative of the equation? Thanks
• Mar 29th 2006, 02:05 AM
Aradesh
yes, that's right, you need to differentiate it.
let
$f(x) = 2x^2-12x+14$
when $x = 1$
$f(x) = 2-12+14 = 4$
so the point (1,4) does lie on the curve.
$f'(x) = 4x-12$
$f'(1) = 4-12 = -8$
so the gradient of the curve at (1,4) is -8.
you could also find the equation of the tangent line that touches the curve at (1,4) but i don't think that's what you need to do.
• Mar 29th 2006, 09:02 PM
classicstrings
Yeah the equation is y = -8x + 12 after simple substitution. Thanks!