Can you find a and b so that the function f(x)= -tanx if xpi/4 is differentiable at x=pi/4? (It's greater than or equal to for the second part)

Question

Can you find a and b so that the function
f(x)=   -tanx if x<pi/4
           -a+bx if x>pi/4 

is differentiable at x=pi/4?

(It's greater than or equal to for the second part)

xapproachesinfinity · Answer

well you just apply derivative definition
from left and right
since it is differentiable at the point of the problem pi/4
then the two derivatives have to be equal

noelgreco · Answer

You still need this?

anonymous · Answer

Yes I do. So I would plug in pi/4 and for both equations and set them equal to each other?

noelgreco · Answer

It requires calculus, as you probably know.  What would be the slope of the tangent function at x = pi/4?

anonymous · Answer

It would be the limit of the slope of the secant line.. which would be $$\lim h \rightarrow0   f(x _{1}+h)-f(x _{1}) / h$$
But to find the slope, would I find the derivative at x=pi/4?
Really confused

xapproachesinfinity · Answer

you don't need all that
just do right derivative of f(x) and left derivative
since f is differentiable at the point pi/4
the two derivative (right and left side of pi/4) should equal each other
then solve for a,b
you will need one more piece of information here f(pi/4) to get a