Everything Maths Grade 12

CHAPTER 7. DIFFERENTIAL CALCULUS 7.6

y

3 x 4 x

5 x

(a) Show that y =

1200 cm^2 − 4 x^2

5 x

.

(b) Find the value of x for which the block will have a maximum volume. (Volume = area of

base× height.)

3. The diagram showsthe plan for a verandawhich is to be built onthe corner of a cottage.A
   railing ABCDE is to be constructed around the four edges of the veranda.

C

B A

D

F

E

cottage

verandah

y

x

If AB = DE = x and BC = CD = y, and the length of therailing must be 30 m, find the

values of x and y for which the verandahwill have a maximum area.

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(1.) 01g4 (2.) 01g5 (3.) 01g6

Rate of Change Problems EMCBO

Two concepts were discussed in this chapter: Average rate of change =f(bb)−−fa(a)and Instantaneous

rate of change = limh→ 0 f(x+hh)−f(x). When we mention rate of change, the latter is implied. Instan-