Find the derivative using the definition of the function f(x) = 7x + 10. Using limits.

Answer 1

f(x+h) = 7(x+h)+10

= 7x + 7h + 10

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

[ 7x + 7h + 10] - (7x+10)

= 7h

the difference quotient:

[f(x+h)-f(x)]/h =

7h/h

= 7

the limit of (the constant) 7 is 7

as h tends to ZER0

so the derivative is 7, which

agrees with the power rule