Find the values of x such that f(x) is decreasing function: f(x)=… - Vidyadip

Question

Find the values of $x$ such that $f(x)$ is decreasing function:
$f(x)=x^4-2 x^3+1$

✓

Answer

$
\begin{aligned}
& f(x)=x^4-2 x^3+1 \\
& \therefore f^{\prime}(x)=\frac{d}{d x}\left(x^4-2 x^3+1\right) \\
& =4 x^3-2 \times 3 x^2+0 \\
& =4 x^3-6 x^2
\end{aligned}
$
$f$ is decreasing, if $f^{\prime}(x)<0$
i.e. if $4 x^3-6 x^2<0$
i.e. if $x^2(4 x-6)<0$
i.e. if $4 x-6<0 \ldots \ldots\left[\because x^2>0\right]$
i.e. if $x<\frac{3}{2}$
i.e. $-\infty<x<\frac{3}{2}$
$\therefore f$ is decreasing, if $-\infty< x <\frac{3}{2}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Applications of Derivatives (p-1)→Applications of Derivatives (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

If p and q are true and r and s are false, find the true value of each of the following statements : (p → q) ∨ (r ∧ s)

For each of the following matrices, find its transpose and state whether it is symmetric, skew-symmetric or neither:
$\left[\begin{array}{ccc}2 & 5 & 1 \\ -5 & 4 & 6 \\ -1 & -6 & 3\end{array}\right]$

Solve the following : If $x =a\left(1-\frac{1}{t}\right), y =a\left(1+\frac{1}{t}\right)$, then show that $\frac{d y}{d x}=-1$

Given that $\sum p_0q_0 = 130, \sum p_1q_1 = 140, \sum p_0q_1 = 160$, and $\sum p_1q_0 = 200$, find Laspeyare’s, Passche’s, Dorbish-Bowely’s and Mashall-Edegeworth’s Price Inbox Numbers.

Find the expected value and variance of the r.v. X if its probability distribution is as follows.

X	1	2	3
P(X=x)	1/5	2/5	2/5

Prepare the truth tables for the following statement patterns : (p ∧ r) → (p ∨ ~q)

With proper justification, state the negation of the following.

(p ↔ q) v (~ q → ~r)

Evalute : $\int x \sqrt{1+x^2} d x$

A property worth ₹ 4,00,000 is insured with three companies. A, B, and C. The amounts insured with these companies are ₹ 1,60,000, ₹ 1,00,000 and ₹ 1,40,000 respectively. Find the amount recoverable from each company in the event of a loss to the extent of ₹ 9,000.

If $X$ has Poisson distribution with $m = 1$, then find $P(X ≤ 1)$ given $e^{-1} = 0.3678.$