Question

Suppose a function f is differentiable everywhere. if f(3)=9 and f'(3)=5 then what is the y-intercept of the tangent line at the point (3,9)?

Answer 1

The y-intercept of the tangent line at the point (3,9) is -6.

Step-by-step explanation:

The y-intercept is the point where the graph of a function intersects the y-axis. To find the y-intercept of the tangent line at the point (3,9), we can use the formula for the equation of a line, y = mx + b, where m is the slope and b is the y-intercept.

Given that f'(3) = 5, the slope of the tangent line at (3,9) is 5. We can substitute the values into the equation y = mx + b, where x = 3, y = 9, and m = 5, to find b (the y-intercept).

Plugging in the values, we get 9 = 5(3) + b. Solving for b, we have b = 9 - 15 = -6. Therefore, the y-intercept of the tangent line at the point (3,9) is -6.