- #1

karush

Gold Member

MHB

- 3,269

- 5

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...