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  • Let the f :R→R be defined by f (x) = 2x + cosx, then f : A. has a minimum at x = π B. has a maximum, at x = 0 C. is a decreasing function D. is an increasing function

Let the f :R\rightarrow R be defined by f (x) = 2x + cosx, then f(x) :
A. has a minimum at x = π
B. has a maximum, at x = 0
C. is a decreasing function
D. is an increasing function

Answers (1)

Given f (x) = 2x + cosx  if f :R\rightarrow R

Apply the first derivative and get

\begin{aligned} &f(x)=\frac{d(2 x+\cos x)}{d x}\\ &\text { Apply the sum rule and } 0 \text { is the derivative of the constant, so }\\ &\Rightarrow f(x)=\frac{d(2 x)}{d x}+\frac{d(\cos x)}{d x} \end{aligned}

Apply power rule and get

\Rightarrow f'(x)=2-sin x

Now, 1 is the maximum value of sin x.

So f'(x)>0, \forall x

So, function f is an increasing function.

So the correct answer is option D.

Posted by

infoexpert22

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