the graph of f(x)=e^sin(x)-2 crosses the x-axis at the point on the interval [0,1]. The slope of f(x) at this point is?

Question

AP Calculus Help!

Answer 1

Evaluate f'(x) at the point of interest, and that will give the slope of the tangent line at that point.

 

f(x) = e^sin(x) - 2

 

f'(x) = e^sin(x)cos(x)

 

At the point of interest,

 

e^sin(x) = 2

 

sin(x) = ln2

 

x = arcsin(ln2)

 

Be sure to work in radians.  Plug this value of x into f'(x), evaluate, and simplify.  You can finish from here.