The total number of local maxima and local minima of the function f(x)=((2-x)/π) cos (π x+3 π)+(1/π2) sin (π x+3 π), where 0

Question

The total number of local maxima and local minima of the function f(x)=((2-x)/π) cos (π x+3 π)+(1/π2) sin (π x+3 π), where 0 < x < 4 is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f'(x)=(2-x) sin (π x) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/d895a50305bf77ea86e1a8183fd2877d-.png" /> ∴ Local maximum at x=1 and local minimum at x=3.

Q. The total number of local maxima and local minima of the function $f (x) = \frac{( 2 - x )}{π} cos (π x + 3 π) + \frac{1}{π ^{2}} sin (π x + 3 π)$ , where $0 < x < 4$ is equal to

$f^{'} (x) = (2 - x) sin (π x)$

$∴$ Local maximum at $x = 1$ and local minimum at $x = 3$ .

Q. The total number of local maxima and local minima of the function f(x)=π(2−x)​cos(πx+3π)+π21​sin(πx+3π), where 0<x<4 is equal to

f′(x)=(2−x)sin(πx) ∴ Local maximum at x=1 and local minimum at x=3.

Q. The total number of local maxima and local minima of the function $f (x) = \frac{( 2 - x )}{π} cos (π x + 3 π) + \frac{1}{π ^{2}} sin (π x + 3 π)$ , where $0 < x < 4$ is equal to

$f^{'} (x) = (2 - x) sin (π x)$

$∴$ Local maximum at $x = 1$ and local minimum at $x = 3$ .