How do I find the derivative of this?

Question

of

f(x)= sq rt. (7-3x)

using the delta definition of a derivative....
the whole
(f(x+h)-f(x))/h

Thanks!

Answer 1

change it to (7-3x)^1/2, then just solve it as you normally would

Answer 2

You use the trick known as multiplying and dividing by the conjugate. The conjugate of sqrt(A) - sqrt(B) is sqrt(A) + sqrt(B). It's useful because

(sqrt(A) - sqrt(B))(sqrt(A) + sqrt(B)) = A - B.

f'(x) =
lim(h->0) [f(x+h) - f(x)] / h =
lim(h->0) [sqrt(7-3(x+h)) - sqrt(7-3x)] / h =
lim(h->0) [sqrt(7-3(x+h)) - sqrt(7-3x)] / h * [sqrt(7-3(x+h)) - sqrt(7-3x)] / [sqrt(7-3(x+h)) - sqrt(7-3x)] =
lim(h->0) [(7-3(x+h)) - (7-3x)] / [h*(sqrt(7-3(x+h)) + sqrt(7-3x))] =
lim(h->0) -3h / [h*(sqrt(7-3(x+h)) + sqrt(7-3x))] =
lim(h->0) -3 / (sqrt(7-3(x+h)) + sqrt(7-3x)) =
-3 / (sqrt(7-3x) + sqrt(7-3x)) =
-3 / (2*sqrt(7-3x)).

Answer 3

damn. i would just use the power rule. are you sure the definition doesn't have a limit attached to it?

power rule:
f(x)=(7-3x)^0.5
f'(x)= [0.5(7-3x)^-0.5] * -3
= 1.5 (7-3x)^-0.5

definition of a derivative
[((7-3x)^0.5)+h]-(7-3x)^0.5)
______________________ = ?
h
sorry if i didn't help but i wish you luck!!

Answer 4

odnt know only in algebra one