New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Application of Derivatives question

2023 · 15 Apr · Shift 1 · Q42

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

PYQ Library
JEE Main
Mathematics
Application of Derivatives
2023 · 15 Apr · Shift 1 · Q42

Application of Derivatives question

2023 · 15 Apr · Shift 1 · Q42

JEE MainMathematicsApplication of DerivativesNumerical+4 / −1

Consider the triangles with vertices

A(2,1), B(0,0)

and

C(t, 4), t \in[0,4]

. If the maximum and the minimum perimeters of such triangles are obtained at

t=\alpha

and

t=\beta

respectively, then

6 \alpha+21 \beta

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Application of Derivatives

Let $x = 2$ be a local minima of the function $f (x) = 2 x^{4} - 18 x^{2} + 8 x + 12, x \in (- 4, 4)$ . If M is local maximum value of the function $f$ in ( $- 4, 4)$ , then M =2023 · MCQ
Let $f : (0, 1) \to R$ be a function defined $f (x) = \frac{1}{1 - e ^{- x}}$ , and $g (x) = (f (- x) - f (x))$ . Consider two statements (I) g is an increasing function in (0, 1) (II) g is one-one in (0, 1) Then,2023 · MCQ
Let the function $f (x) = 2 x^{3} + (2 p - 7) x^{2} + 3 (2 p - 9) x - 6$ have a maxima for some value of $x 0$ . Then, the set of all values of p is2023 · MCQ
If the functions $f (x) = \frac{x ^{3}}{3} + 2 b x + \frac{a x ^{2}}{2}$ and $g (x) = \frac{x ^{3}}{3} + a x + b x^{2}, a e q 2 b$ have a common extreme point, then $a + 2 b + 7$ is equal to :2023 · MCQ
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