1. ## need help

Consider $\displaystyle f(x)=x^{1/2}$. Find all value(s), c, in the interval [0,1] such that the slope of the tangent line to the graph of f at c is parallel to the secant line through the point (0, f(0)) and (1, f(1)).

$\displaystyle \frac{1}{2x^{1/2}}$
and slope of (0. f(0)) and (1,f(1)) is 1
This is all i can do, need help on this

2. well you took the derivative correctly ad you know the required slop is equal to 1

$\displaystyle \frac{1}{2\sqrt{x}}=1$

just solve that equation.

3. Hello, Bryan!

You're almost there . . .

Consider $\displaystyle f(x)\:=\:x^{\frac{1}{2}}$.
Find all value(s), $\displaystyle c$, in the interval [0,1] such that the slope of the tangent line
to the graph of $\displaystyle f$ at $\displaystyle c$ is parallel to the secant line through: $\displaystyle (0,\,f(0))$ and $\displaystyle (1, f(1))$.

The slope of the tangent is: .$\displaystyle \frac{1}{2x^{\frac{1}{2}}}$ . . . . Yes!

. . and slope of (0, f(0)) and (1, f(1)) is 1 . . . . Right!

So when is: .$\displaystyle \frac{1}{2\sqrt{x}}$ equal to $\displaystyle 1$?