Find equation of the straight line tangent to the curve at the point indicated:
$y=2x^2 -5$ at $(2,3)$
I think I have to use $y=m(x-x_o)+y_0$ etc but I'm not sure how to find the $m$! Thanks for tips/solutions!
[Math] Find equation of the straight line tangent to the curve at the point indicated
algebra-precalculuscalculus
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Best Answer
$$y=2x^2-5$$ We can differentiate this equation to give us the slope, $m$. $$m=4x$$ If we input our $x$ value of $2$, we should get $m=8$ at $(2,3)$. We can now use the general equation for a line using the values for $m$ and from the point $(x_1,y_1)$. $$y-y_1=m(x-x_1)$$ $$y-3=8(x-2)$$ This gives us our final answer for the tangent line. $$y=8x-13$$