Maxima and MinimaMedium
Question
Let $f(x) = x^{2025} - x^{2000},x \in \lbrack 0,1\rbrack$ and the minimum value of the function $f(x)$ in the interval $\lbrack 0,1\rbrack$ be $(80)^{80}(n)^{- 81}$. Then n is equal to
Options
A.-81
B.-40
C.-41
D.-80
Solution
$f(x) = x^{2025} - x^{2000}$
$f'(x) = 0 \Rightarrow x = \left( \frac{2000}{2025} \right)^{1/25} = \alpha($ say $)$
$$\therefore f(0) = 0,f(1) = 0,f(\alpha) = \left( \frac{80}{81} \right)^{80} \cdot \frac{- 1}{81} = 80^{80} \cdot ( - 81)^{- 81}$$
Create a free account to view solution
View Solution FreeMore Maxima and Minima Questions
In a regular triangular prism the distance from the centre of one base to one of the vertices of the other base is l. Th...If a continuous function f (x) has a local maximum at x = a, then -...The point on the curve x2 = 2y which is nearest to (0, 5) is-...If xy = c2 then the minimum value of ax + by (a > 0, b > 0) is -...Function x - sin x has-...