Find the slope of the curve y = 3X. + 2.0 — x’ at the point (-1, 0).
2 Find ‘II for: ax (i) y = —3In xs (ii) y = In(7x) (iii) y = In(x-3) (iv) y = e-3x (v) y = sin —2x + Seim ir _ 1 t Ivi)v – se, 4e”
3. It takes 1500 minutes to fill a petrol storage tank at a service station. The volume V litres. of petrol in the tank after time I minutes, is given by
V = 500t t2, for 0 5 t 5 1500
(i) Find the instantaneous rate of change of volume when f = 300 (ii) Find the volume of petrol in the tank when the instantaneous rate of change of volume is 100 litres/minute. (Ili) Find the instantaneous rate of change of volume when the volume of petrol in the tank is 240000 litres. (iv) How much petrol is in the tank when it is full?
4. For each of the following functions find the a and y co-ordinates of the stationary points. Then classify each of the stationary points as a local ma vanum, a local minimum, or a horizontal point of Inflection (using the First Derivative Test).
(i) y = —4×2 + 16x — 10 (11) y= x3 — 3×2 + 9x + I (ill) y = x3 — 2×2 — 12x