# tangent line problems

• Nov 22nd 2011, 08:43 AM
angelamonique
tangent line problems
a) Find an equation on the tangent line to the graph of y=g(x) at x= 5 if g(5) = -3 and g'(5) = 4

b) If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4)
• Nov 22nd 2011, 08:49 AM
TheChaz
re: tangent line problems
Use the point slope formula...

\$\displaystyle y - y_1 = m(x - x_1)\$

The point \$\displaystyle (x_1 , y_1) = (5, -3)\$

The slope is 4.
• Nov 22nd 2011, 08:51 AM
Plato
re: tangent line problems
Quote:

Originally Posted by angelamonique
a) Find an equation on the tangent line to the graph of y=g(x) at x= 5 if g(5) = -3 and g'(5) = 4

b) If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4)

The tangent line at \$\displaystyle (x_0,g(x_0))\$ is \$\displaystyle y-g(x_0)=g'(x_0)(x-x_0)~.\$
• Nov 22nd 2011, 09:00 AM
angelamonique
re: tangent line problems
Thank you, but can you also tell me how you figured that out?
• Nov 22nd 2011, 12:35 PM
HallsofIvy
Re: tangent line problems
They attended class! One of the basic definitions of the derivative is that it is the slope of the tangent line.
• Nov 22nd 2011, 01:53 PM
TheChaz
Re: tangent line problems
Quote:

Originally Posted by HallsofIvy
They attended class! One of the basic definitions of the derivative is that it is the slope of the tangent line.

I wasn't sure exactly how to approach that!

Indeed, the veracity/validity/whatever of the point slope formula should not be called into question at this juncture. So we're left with the task of finding a point and a slope, in order to determine the desired line.
Welp, g(5)=-3 means that (5, -3) is the point.
And you really DO need to know that the slope of the tangent is given by the derivative.