Let the function f(x) be defined as follows f(x)= begincasesx3+x2-10 x, -1 ≤ x

Question

Let the function f(x) be defined as follows f(x)= begincasesx3+x2-10 x, -1 ≤ x<0 cos x, 0 ≤ x<π / 2 1+ sin x, π / 2 ≤ x ≤ π endcases Then f(x) has (A) a local minimum at x=π / 2 (B) a global maximum at x=π / 2 (C) an absolute minimum at x=-1 (D) an absolute maximum at x =π

Tardigrade Admin · Accepted Answer

Correct answer is (c) an absolute minimum at x=-1

Q. Let the function $f (x)$ be defined as follows
$f (x) = ⎩ ⎨ ⎧ x^{3} + x^{2} - 10 x, cos x, 1 + sin x, - 1 \leq x < 0 0 \leq x < π /2 π /2 \leq x \leq π$
Then $f (x)$ has

a local minimum at $x = π /2$

a global maximum at $x = π /2$

an absolute minimum at $x = - 1$

an absolute maximum at $x = π$

Correct answer is (c) an absolute minimum at $x = - 1$

Q. Let the function f(x) be defined as follows f(x)=⎩⎨⎧​x3+x2−10x,cosx,1+sinx,​−1≤x<00≤x<π/2π/2≤x≤π​ Then f(x) has

a local minimum at x=π/2

a global maximum at x=π/2

an absolute minimum at x=−1

an absolute maximum at x=π