The correct answer is false.
It is false that the slope of the investment demand function indicates how sensitive investment is to changes in real interest rates. The 'steeper' the investment demand function, the less sensitive investment is to changes in the real rate of interest, all else constant.
We can say that the downward slope is the consequence of several reasons. For instance, the concept that money, its nominal value, is fixed. However, the real value of money depends on the level of prices. So the demand for money is related to the demand for it. The interest rate falls when the price level falls.