Final answer:
To find the value of f(-4), we need to determine the equation of the tangent line passing through the given points. The equation of the tangent line is y + 9 = (3/14)(x + 4). By substituting x = -4 into this equation, we find that f(-4) = -9.
Step-by-step explanation:
In order to find the value of f(-4), we need to determine the equation of the tangent line passing through the point (-4, -9) which also passes through the point (10, -6).
First, let's find the slope of the tangent line by using the formula: slope = (change in y)/(change in x). The change in y is -6 - (-9) = 3 and the change in x is 10 - (-4) = 14. So, the slope is 3/14.
Next, we can use the point-slope form of a linear equation to find the equation of the tangent line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get: y - (-9) = (3/14)(x - (-4)). Simplifying, we get y + 9 = (3/14)(x + 4).
Now, we can find f(-4) by substituting x = -4 into the equation of the tangent line. Plugging in -4 for x, we get y + 9 = (3/14)(-4 + 4), which simplifies to y + 9 = 0. Solving for y, we find that y = -9.