Just another maths question (1 Viewer)

[DeathB4Life]

"The stock value of a company over the first 10 days of it being sold fluctuates according to the formula:

V=[t(t-7)^2] + 4

Where V is the value, in cents, of each share and t is the number of days after the intitial sale.

a. Find all extreme points in the first 10 days and their nature.

b. Find the point/s of inflection

c. Sketch the graph of V versus t for the first 10 days."

im stuck on just finding the min/max points:

product rule to differentiate t(t-7)^2

[2t(t-7)^2] + (t-7)^2

expanded:
= (t^2) - 14t + 49 + (2t^3) - (28t^2) + 98t
= (2t^3) - (27t^2) -42t + 49

how would i go about finding the stationary points?

 

[Trev]

V = t.(t-7)²+4
dV/dt = t.2(t-7)+(t-7)² = (t-7)(2t+t-7) = (t-7)(3t-7).
Stationary points where dV/dt=0 so where t=7 or t=7/3 days.

You differentiated wrong.
To find the nature of these points test the gradient either side of each point.
To find points of inflection, diferentiate again.