calc QUES ANSWER PLS

Question

If the tangent line to y = f(x) at (7, 3) passes through the point (0, 2), find f(7) and f '(7).

Answer 1

The answers are simple, provided you think about the question correctly. Notice you already have the value of f(x) when x = 7. It's 3, because we have the coordinates (7, 3). So f(7) = 3.

To find f'(7), because the derivative is slope, find the slope of the line that passes through the two points, using the slope formula.

f'(7) = (2 - 3)/(0 - 7) = -1/-7 = 1/7

Or, a more complex solution is to find the equation of the line that passes through the two points, and then find the equation's derivative. That goes like this:

y = mx + b

y = (1/7)x + 2

y is the same as f(x). So f'(x) = 1 * (1/7)x^0 = 1/7. Let me know if this is helpful!

Answer 2

(7,3) is on the graph of f(x)

f(7) = 3

f'(7) = (3 - 2) / (7 - 0) The slope of the tangent line.