JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

Let

f(x)=-x^3+a x^2+b x+5 \sin x \cos x

be a decreasing function on the set

R

. Then,

a

and

b

satisfy

View answer and explanation

Correct option: B

a^2+3 b+15 < 0

Option B (

a^2+3 b+15 < 0

) is correct because for the function to be decreasing, its derivative must be negative, leading to the given inequality.

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f\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}}

x

f\left( x \right) = {x^2} + ax + 1

a

f(x)=

\sin x-\cos x-a x+b

f(x)=x e^{x(1-x)}, x \in R

f

g

fog

f\left( x \right) = {x^3} + b{x^2} + cx + d

0 < {b^2} < c

\left( { - \infty ,\;\infty } \right)