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

Since y=3x+4 is is the slope of the tangent line, it is actually the 1st derivative of f(x). That means f(x) is an antiderivative of 3x+4. So f(x) = 3/2 x²+4x+C. The fact that f(x) passes through (3,10) means that when x = 3, f(x)=10. Substitute those values to find C.

After trying the above check here:

desmos.com/calculator/hrp6ydjxri

The above graph uses f(x)=3x+4 and F(x) for the original function.