Question

Find the curve y=f(x) in the xy-plane that passes through the point (9,4) and whose slope at each point is 3`sqrt((x))` ?

Answer 1

`f(x) = 2x^(3/2) - 50`

Explanation:

Since the slope of the line is given by the derivative, the curve `f(x)` is given by integrating `3sqrt(x)`.

`F(x) = 3sqrt(x) = 3x^(1/2)`

`f(x) = int F(x) dx = 2x^(3/2) +C`

The value of `C` is `4 = 2(9)^(3/2) + C -> 4 - 54 = C -> C = -50`

The equation is therefore `f(x) = 2x^(3/2) - 50`

Hopefully this helps!