How do you find the equation of the tangent line to the curve #f(x) = x^2 + 5x# at x = 4?

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Answer 1 · 2016-03-09T18:06:31

Like this:

#f(x)=x^2+5x#

#:.f'(x)=2x+5#

This gives the gradient #m# of the tangent line.

If #x=4# then #m=(2xx4)+5=13#

To get the #y# point:

#f(4)=4^2+(5xx4)=16+20=36#

The tangent line is of the form #y=mx+c#

#:.36=(13xx4)+c#

#:.c=36-52=-16#

So the equation of the tangent line#rArr#

#y=13x-16#

graph{(13x-16-y)(x^2+5x-y)=0 [-64.1, 64, -32, 32.1]}