Grade 12 maths note

1. Ch-4 Applications of
derivatives
Ethiopian G-12 maths

2. Contents of the unit

3. Extreme values of Function
Revision on zeros of function
Critical numbers and critical values

4. Revision on zeros of function
✓A number c is the zero of function. If and only if f(c)=0.
Example: Find the real zeros of function
a) f(x)=𝑥3
− 8
Ans c=2
a) g(x)=7𝑥2
− 51𝑥 + 14
Ans c=7,2/7
a) h(x)=
𝑥2−8𝑥+7
𝑥2+1
Ans c=1.7

5. Critical numbers and critical values
Extreme value Theorem

6. Example
➢Is continuous on (1,5) but has no local extremum
values .
𝑓 𝑥 = 4𝑥 + 2
✓Is not continuous on (-2,2)
✓So it has no extremum values
𝑓 𝑥 =
5
𝑥
❖It has only local maximum on (1,5]
❖It has only local minimum on[1,5)
❖It has both local extremum on [1,5]
𝑓 𝑥 = 6𝑥 + 2

7. Examples
(cont……)
Find critical number of given function.
1. 𝑓 𝑥 = 4𝑥2 − 5𝑥2 − 8𝑥 + 20
2. 𝑓 𝑥 = 5𝑥 − 2 3𝑥