Question

f(x) =

5, x< or=2
ax + b, 2 < x < 10
21, x> or = 10

is continuous for all x

Find values a and b

@rational

Answer 1

For f(x) to be continuous at x=a we must have :

LHL = RHL = f(a)

Answer 2

```
5, x <=2
ax + b, 2 < x < 10
```

using LHL = RHL, get an equation for f(x) to be continuous at x=2

Answer 3

So we can make two equations

5 = 2a +b
and
21 = 10a + b?

Answer 4

thats it!

Answer 5

wonderful xD

So that means I just solve by subtracting 10 a + b = 21 and 2a + b = 5

-> 8a = 16
or a = 16/8

a = 2

5 = 2(2) + b

5 = 4 + b

b = 1

Am I right? this question is for 4 marks, on my exam day(18th this month)

Answer 6

once you setup the equations, you're free to solve it using any method you like

Answer 7

a=2, b=1 looks good!

Answer 8

Awesome :) I might have 2 more question types under this section, is it too much trouble to ask?

Answer 9

feel free to tag me in all your questions.. these are fun :)