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Find an equation of the tangent line to the graph of
y = g(x) at x = 4 if g(4) = −3 and g'(4) = 2.
(Enter your answer as an equation in terms of y and x.)

Respuesta :

Answer:

[tex] y- y_o = m(x-x_o) [/tex]

For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:

[tex] y -(-3) = 2 (x-4)[/tex]

And if we reorganize the terms we have:

[tex] y+3 = 2x -8[/tex]

And subtracting 3 in both sides we got:

[tex] y = 2x -11[/tex]

Step-by-step explanation:

For this case we have the following function y=g(x) and we want to find the tangent line to this function using the conditions: [tex] g(4) =-3, g'(4)=2[/tex]

So we need a function like this one:

[tex] y- y_o = m(x-x_o) [/tex]

For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:

[tex] y -(-3)=2(x-4)[/tex]

And if we reorganize the terms we have:

[tex] y+3 = 2x -8[/tex]

And subtracting 3 in both sides we got:

[tex] y = 2x -11[/tex]

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