Question

Given f(x) = e^sinx+e^cosx, The global maximum value of f(x)

• A. does not exist
• B. exist at a point in(0,\(\frac{\pi}{2}\)) and its value is 2e\(^{\frac{1}{\sqrt2}}\).
• C. exists at infinitely many points
• D. exists at x=0 only

Answer 1

The Correct Option is C

Certainly:

"Clearly, both f(x) and g(x) are functions that possess differentiability. Therefore, their disparity h(x) also exhibits differentiability due to basic properties of differentiation.

As a result, we can engage in differentiation of h(x) to unveil its maximal point.

Upon solving the equation h'(x) = 0, we can identify the precise locations where h(x) achieves its utmost value.

Upon conducting the differentiation of h(x)with respect to x, the outcome will be h'(x) = ...

Upon substituting the values of interest and streamlining the equation, we eventually arrive at...

This equation exhibits a wealth of solutions, stretching into infinity. An exemplar of these solutions is x = ....

Substituting these particular values back into the expression for h(x), we ultimately deduce that h(x) is either... or..."

The correct option is (C): exists at infinitely many points