If p≥1p≥1, the graphs of w=sinxw=sin⁡x and w=pe−xw=pe−x intersect for x≥0x≥0.
Find the smallest value of pp for which the graphs are tangent.
Solution
For w=sinxw=sin⁡x, dwdxdwdx=
Your last answer was interpreted as follows: cosx
This answer is invalid. Forbidden variable or constant: cosx.
For w=pe−xw=pe−x, dwdxdwdx=
Equating the equations of the curves and those of the derivatives yield two equations involving xx and pp. Solving these equations, the smallest value of xx is obtained as
Therefore the corresponding value of (p(p is (write your answer in the form pp=value)