Is this differentiation right.
question:
(2x-5)^3
My Answer:
6(2x-5)^2
If I do this how do I find the gradient. If I sub x=0 i don't get what I want.
Please help.
The differentiation is correct.
That is the curve gradient for any x.
If you sub in x=0, you get the slope of the tangent to the curve at x=0,
but not the slope of the tangent that passes through the origin if that's what you were looking for.
What were you trying to calculate ?
Well then do as you are instructed.
The find where the curve cuts the $\displaystyle x$ axis, let $\displaystyle y = 0$.
So $\displaystyle 0 = (2x - 5)^3$
$\displaystyle 2x - 5 = 0$
$\displaystyle x = \frac{5}{2}$.
So you are not evaluating the derivative at $\displaystyle x = 0$. You are evaluating the derivative at $\displaystyle x = \frac{5}{2}$.