Question

Let f(x) = 10x + 12 - 17eˣ. Then the equation of the tangent line to the graph of f(x) at the point (0, - 5) is given by y = mx + b for m = b

Answer 1

The equation of the tangent line to the graph of f(x) at the point (0, -5) is y = -7x - 5.

Step-by-step explanation:

The tangent line to the graph of f(x) at the point (0, -5) can be found by finding the first derivative of f(x) and evaluating it at x = 0. The slope of the tangent line is equal to the value of the first derivative at that point, which represents the rate of change of the function at that point.

1. Find the derivative of
   `f(x): f'(x) = 10 - 17e^x`
2. Evaluate the derivative at
   `x = 0: f'(0) = 10 - 17e^0 = 10 - 17 = -7`
3. The slope of the tangent line is -7, so the equation of the line is y = -7x + b
4. Substitute the coordinates of the given point (0, -5) into the equation to find the value of b: -5 = -7(0) + b, b = -5
5. The equation of the tangent line is
   `y = -7x - 5`