Given that the graph of f(x) passes hrough the point (3,10) and that the slope of its tangent line at (x, f(x)) is 3x + 4, what is f(4)?

Question

Given that the graph of f(x) passes hrough the point (3,10) and that the slope of its tangent line at (x, f(x)) is 3x + 4, what is f(4)?

Answer 1

The formula for the slope of the tangent line is the derivative of the original function. The goal is to define the original function f(x) so that we can find f(4).

The original function must be an antiderivative of 3x + 4, so f(x) = 3x²/2 +4x + C. To find the value of C, use the fact that when x = 3, y = 10.

You are not requested to write the equation of the tangent line at (3,10), but if you were, its slope would be 3(3) + 4= 13, so its equation would be y-10 = 13(x-3).

Left to you do determine the value of C and then find f(4).

Having done so, check your result here:

desmos.com/calculator/jkuyypw5hz