Figure 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$\mathrm{a}=\mathrm{vdv}/\mathrm{ds},$ 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