Question

If `g(x) = x^2 + bx`, and the tangent to the function at `x = -1` is parallel to the line that goes through `(3, 4)` and `(0, -2)`, what is the value of `b`?

Answer 1

`b = 4`

Explanation:

Start by finding the derivative of `g(x)`.

`g'(x) = 2x + b` since `b` is a constant

Find the slope between the two points now.

`m = (y_2 - y_1)/(x_2 - x_1) = (4 - (-2))/(3 - 0) = 6/3 = 2`

The tangent to `g(x)` at `x= -1` is given by:

`g'(x) = -2 + b`

Since we are given that the tangent line is parallel to the line that passes through the same points, we know the tangent line will have the same slope.

`2 = -2 + b`

`4 = b`

Hopefully this helps!