Let f ( x ) = e x − 2 x for 1 ≤ x ≤ 2 , and f ( x ) = 2 sin x + x for 2 < x ≤ 2 π . Find the least value on [ 1 , 2 π ] to two decimals.

Start Free Mock LoginAlready registered? Login here

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minQB

MathematicsMediumnumerical

Let $f (x) = e^{x} - 2 x$ for $1 \leq x \leq 2$ , and $f (x) = 2 sin x + x$ for $2 < x \leq 2 π$ . Find the least value on $[1, 2 π]$ to two decimals.

Answer:

0.72

Solution:

On $[1, 2], e^{x} - 2 x$ is increasing, so its minimum is $e - 2 \approx 0.71828$ . On $(2, 2 π]$ , stationary/end-point checks give larger values. Hence the least value is 0.72 to two decimals.

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...