1. $\tiny{3.2.15}$
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function the secant line through the endpoints, and the tangent line at $(c,f(c))$.
$f(x)=\sqrt{x} \quad [0,4]$
Are the secant line and the tangent line parallel?
$\dfrac{{f(b)-f(a)}}{{b-a}}$
then
$f(0)=0 \quad f(4)=2 \quad m=\dfrac{1}{2}$
then
$f'(x)=\dfrac{1}{2\sqrt{x}} =\dfrac{1}{2}\quad\therefore \quad f'(1)=\dfrac{1}{2}$
then
$(c,f(c))=(1,1)$

ok not sure if this is the de jour way but.......  Reply With Quote

2.

3. Originally Posted by karush $\tiny{3.2.15}$
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function the secant line through the endpoints, and the tangent line at $(c,f(c))$.
$f(x)=\sqrt{x} \quad [0,4]$
Are the secant line and the tangent line parallel?
$\dfrac{{f(b)-f(a)}}{{b-a}}$
then
$f(0)=0 \quad f(4)=2 \quad m=\dfrac{1}{2}$
then
$f'(x)=\dfrac{1}{2\sqrt{x}} =\dfrac{1}{2}\quad\therefore \quad f'(1)=\dfrac{1}{2}$
then
$(c,f(c))=(1,1)$

ok not sure if this is the de jour way but.......
It's fine, well done.  Reply With Quote

4. "De jour" way? Do you think the correct way to do a problem changes from day to day?  Reply With Quote

5. Originally Posted by HallsofIvy "De jour" way? Do you think the correct way to do a problem changes from day to day?
I think the OP just means they are not sure if this is considered the most concise or elegant way, or if there are any steps that are not mathematically justified.  Reply With Quote

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