Question

Please answer clearly

Answer 1

(a) f(x + h) = - 5x - 5h + 2 , difference quotient = - 5

Explanation:

(a)

to find f(x + h) , substitute x = x + h , into f(x)

f(x) = - 5x + 2 , then

f(x + h) = - 5(x + h) + 2

= - 5x - 5h + 2

(b)

Then the difference quotient is

`(f(x+h)-f(x))/(h)` ← substitute f(x + h) and f(x) into the quotient

=
`(-5x-5h+2-(-5x+2))/(h)`

=
`(-5x-5h+2+5x-2)/(h)` ( collect like terms on numerator )

=
`(-5h)/(h)` ( cancel out h on numerator/ denominator )

= - 5