If we know the slope at each point is 3 square roots of X, that's what our Y prime is, because our slope is our first derivative. So Y prime equal 3 square roots of X. If we take the integral, we get integral Y prime DX equal the integral of 3X to the half DX so Y equal. Add 1 to the exponent and divide by the new exponent. So Y equal 2X to the three halves plus our C We were given the .47. So putting 4IN for X and seven in for Y, solving for C, we get Y equal 2X to the three halves -9.