M L Aggarwal Solutions for Chapter: Applications of Derivatives, Exercise 6: EXERCISE 7.6

Find the (absolute) maximum and the (absolute) minimum values of the following functions in the indicated intervals. Also find the points of (absolute) maxima and minima:

$f\left(x\right)=4x-\frac{1}{2}{x}^2$ in $\left[-2, \frac{9}{2}\right]$

Find the (absolute) maximum and the (absolute) minimum values of the following functions in the indicated intervals. Also find the points of (absolute) maxima and minima:

$f\left(x\right)=2x^3-15x^2+36x+1$ on the interval $\left[1,5\right]$

Find the (absolute) maximum and the (absolute) minimum values of the following functions in the indicated intervals.Also find the points of (absolute) maxima and minima:

$f\left(x\right)={\left(\frac{1}{2}-x\right)}^2+x^3$ in $\left[-2, 2.5\right]$

Find the (absolute) maximum and the (absolute) minimum values of the following functions in the indicated intervals. Also find the points of (absolute) maxima and minima:

$f\left(x\right)=3x^4-8x^3+12x^2-48x+25$ in $\left[0,3\right]$

Find the (absolute) maximum and the (absolute) minimum values of the following functions in the indicated intervals. Also find the points of (absolute) maxima and minima:

$f\left(x\right)=x+\sin x$ in $\left[0,2\mathrm{\pi }\right]$

Find the (absolute) maximum and the (absolute) minimum values of the following functions in the indicated intervals. Also find the points of (absolute) maxima and minima:

$f\left(x\right)=\sin x+\cos x$ in $\left[0,\mathrm{\pi }\right]$.

Find the (absolute) maximum and the (absolute) minimum values of the following functions in the indicated intervals. Also find the points of (absolute) maxima and minima:

$f\left(x\right)=3+\left|x+1\right|$ in $\left[-2,3\right]$

Find the maximum and minimum values of $x+\sin 2x$ on $\left[0,2\mathrm{\pi }\right]$. Also find points of maxima and minima.