Applying the Mean Value Theorem with a=2, b=5 to the function in the figure attached inside leads to c=4. What is the equation of the tangent line at 4?

y=________
please explain!! don't know where to start :/

thanks!

Question

Applying the Mean Value Theorem with a=2, b=5 to the function in the figure attached inside leads to c=4. What is the equation of the tangent line at 4?

y=________
please explain!! don't know where to start :/

thanks!

anonymous · Answer

attachment

ganeshie8 · Answer

the slope of tangent at $x = c$, equals the slope of secant

ganeshie8 · Answer

so, slope at x = 4 equals below :

$\large  \frac{11-7}{5-2} $

anonymous · Answer

ohh okay so 5/3?

how can we use that to find b?

ganeshie8 · Answer

you knw slope, and u have the point : $(4, 10)$
u can find the equation of tangent ?

ganeshie8 · Answer

slope = 4/3

anonymous · Answer

oh oops sorry, meant 4/3 haha

so 10=(4/3)(4)+b
10=(16/3) + b

b=14/3 ?

ganeshie8 · Answer

correct !

anonymous · Answer

so the equation would be y=4/3 x + 14/3 ?

ganeshie8 · Answer

$\large \color{red}{\checkmark}$

anonymous · Answer

hehe yay! thank you!! :D

ganeshie8 · Answer

yw !