Figure below shows the velocity-displacement curve for an object moving along a straight line. At which of the points marked is the object speeding up?

From a = v dv/ds, we can find the sign of acceleration at various points. v is positive for all three points 1, 2 and 3 . dv/ds is positive for point 1, zero for point 2, negative for point 3. So, only for point 1, velocity and acceleration have same sign, so the object is speeding up at point 1 only.