Question

find the equation of the tangent line to the curve when x has the given value... f(x)= 5x^2+x ; x=-4

Answer 1

You have to find the gradient function of f first. This will give you the gradient at any point. Then you need to use the point-gradient formula for a straight line. The point you'll be using is the point where the tangent touches the parabola (since a tangent only touches at one point). So the point here is x=-4, f(-4) = 5(-4)^2+(-4) = 76; i.e (-4,76). Your gradient is \[f'(x)=10x+1 \rightarrow f'(-4)=-40+1 = -39\]The equation of the tangent line is then\[y-76=-39(x-(-4)) \rightarrow y = -39x-80\]

Answer 2

Re-check everything - I just saw this question unanswered and stole some time. The theory is right, though :)

Answer 3

yeah that's right thank u:) i just couldnt figure out the steps