Hello,
I need to find the tangent line to the grapg of y=g(x) at x=5 if g(5) = -3 and g'(5) = 4
Can anybody give me a hint how I can do that?
Thanks
that is correct.
The equation for a line can be written like $\displaystyle y=kx+c$
$\displaystyle g'(5)=4$ gives you the slope of the line (k)
and $\displaystyle g(5)=-3$ gives you a point in the tangent line (x and y)
Knowing that,
$\displaystyle -3=4*5+c$
$\displaystyle -3=20+c$
$\displaystyle c=-23$
$\displaystyle y=4x-23$