Question

Find an equation of the tangent line to the graph of

y = g(x) at x = 3 if g(3) = −5 and g'(3) = 4.
(Enter your answer as an equation in terms of y and x.)

Answer 1

The equation of the tangent line to the graph of y = g(x) at x = 3 is y = 4x - 17.

Step-by-step explanation:

To find the equation of the tangent line to the graph of y = g(x) at x = 3, we need to use the values of g(3) and g'(3). Given that g(3) = -5 and g'(3) = 4, we can determine the equation of the tangent line.

The equation of a line can be given in the form y = mx + b, where m represents the slope of the line. Since we are looking for the equation of the tangent line, we know that the slope of the tangent line at any point is equal to the derivative of the function at that point.

So, the equation of the tangent line to the graph of y = g(x) at x = 3 is y = 4x - 17.