New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Application of Derivatives question

2023 · 30 Jan · Shift 2 · Q30

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Application of Derivatives
2023 · 30 Jan · Shift 2 · Q30

Application of Derivatives question

2023 · 30 Jan · Shift 2 · Q30

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

If the functions

f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}

and

g(x)=\frac{x^3}{3}+a x+b x^2, a eq 2 b

have a common extreme point, then

a+2 b+7

is equal to :

A
6
B
$\frac{3}{2}$
C
3
D
4

More from Application of Derivatives

A wire of length $20 m$ is to be cut into two pieces. A piece of length $l_{1}$ is bent to make a square of area $A_{1}$ and the other piece of length $l_{2}$ is made into a circle of area $A_{2}$ . If $2 A_{1} + 3 A_{2}$ is minimum…2023 · MCQ
The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :2022 · MCQ
For the function $f (x) = 4 lo g_{e} (x - 1) - 2 x^{2} + 4 x + 5, x > 1$ , which one of the following is NOT correct?2022 · MCQ
The sum of absolute maximum and absolute minimum values of the function $f (x) = ∣2 x^{2} + 3 x - 2∣ + sin x cos x$ in the interval [0, 1] is :2022 · MCQ
Let $λ^{*}$ be the largest value of $λ$ for which the function $f_{λ} (x) = 4 λ x^{3} - 36 λ x^{2} + 36 x + 48$ is increasing for all x $\in$ R. Then $f_{λ^{*}} (1) + f_{λ^{*}} (- 1)$ is…2022 · MCQ
If the absolute maximum value of the function $f (x) = (x^{2} - 2 x + 7) e^{(4 x^{3} - 12 x^{2} - 180 x + 31)}$ in the interval $[- 3, 0]$ is $f (α)$ , then :2022 · MCQ
The curve $y (x) = a x^{3} + b x^{2} + c x + 5$ touches the $x$ -axis at the point $P (- 2, 0)$ and cuts the $y$ -axis at the point $Q$ , where $y^{'}$ is equal to 3 . Then the local maximum value of $y (x)$ is:2022 · MCQ
The sum of the maximum and minimum values of the function $f (x) = ∣5 x - 7∣ + [x^{2} + 2 x]$ in the interval $[\frac{5}{4}, 2]$ , where $[t]$ is the greatest integer $\leq t$ , is .2022 · Numerical