[SPLIT] find [f(a + h) - f(a)] / h for f(x) = -x^2 + 4

[kjones]

I'm having problems with one more in this section.

Consider the function f(x) = -x^2 + 4

e) Find f(a + h) - f(a)] / h

Thank you.
K

 

[askmemath]

f(x) = -x^2 + 4

f(a+h) - f(a)

-(a+h)^2 + 4 - [-(a)^2 +4]

Can you solvc it from here?

 

[kjones]

Simplified further

Not really, will you help me?

Maybe it works this way...?

. . .[f(a + h) - f(a)] / h

. . .= (-2ah - h^2) / h

. . .= h(2a + h) / h

. . .= ???

K

 

[askmemath]

Re: Simplified further

Eh??

-(a + h)^2 + 4 - [-(a)^2 + 4]

-(a^2 + h^2 + 2ah) + 4 - [-a^2 + 4]

-(a^2 + h^2 + 2ah) + 4 + a^2 - 4

-a^2 - h^2 - 2ah + 4 + a^2 - 4

-h^2 - 2ah

Taking -h common

-h(2a + h)

which is your final answer

 

[kjones]

THANKS

THANKS ...especially for working it step by step...baby steps.

K