Find an equation of the tangent line to the graph of

y = g(x) at x = 5 if g(5) = −3 and g'(5) = 6

Guest Mar 26, 2017

#1**+3 **

g'(5) = 6

This means the slope of the tangent line we're after is 6.

g(5) = -3

This means the tangent line passes through the point (5,-3).

So now all we need to do is simply find the equation for a line with a slope of 6 that passes through the point (5,-3).

y = mx + b

Plug in what we know and solve for what we don't (in this case, b).

-3 = 6(5) + b

-3 = 30 + b

-33 = b

Now use the slope and y intercept to make the equation.

y = 6x - 33

hectictar
Mar 26, 2017