Applications of derivatives

9000070406

Level:

Given function $f(x)= x^{3} + 6x^{2} - 15x + 7$, find the intervals where $f$ is an increasing function.

$\left (-\infty ;-5\right )$

$\left (-\infty ;-3\right )$

$\left (-1;\infty \right )$

$\left (-3;\infty \right )$

9000070407

Level:

Given the function $f(x) = -x^{3} + 3x^{2} + 9x - 1$, find the intervals where $f$ is a decreasing function.

$\left (3;\infty \right )$

$\left (-\infty ;1\right )$

$\left (-1;3\right )$

$\left (1;\infty \right )$

9000070408

Level:

Given the function $f(x) = -x^{3} + 3x^{2} + 45x - 12$, find the intervals where $f$ is an increasing function.

$\left (-3;5\right )$

$\left (-\infty ;-3\right )$

$\left (5;\infty \right )$

$\left (-12;45\right )$

9000070409

Level:

Given the function $f(x) = \frac{x^{2}} {x-2}$, find the intervals where $f$ is a decreasing function.

$\left (0;2\right )$

$\left (-\infty ;-1\right )$

$\left (5;\infty \right )$

$\left (2;5\right )$

9000070410

Level:

Given the function $f(x) = - \frac{x^{2}} {x+3}$, find the intervals where $f$ is an increasing function.

$\left (-3;0\right )$

$\left (-\infty ;-6\right )$

$\left (0;\infty \right )$

$\left (-3;4\right )$

9000079101

Level:

Find the intervals of monotonicity for the following function. \[ f(x)= \frac{3x + 1} {2x - 5} \]

Decreasing on $\left (-\infty ; \frac{5} {2}\right )$ and $\left (\frac{5} {2};\infty \right )$.

Decreasing on $\left (-\infty ; \frac{5} {2}\right )\cup \left (\frac{5} {2};\infty \right )$.

Decreasing on $\left (-\infty ; \frac{5} {2}\right )$, increasing on $\left (\frac{5} {2};\infty \right )$.

Increasing on $\left (-\infty ; \frac{5} {2}\right )$, decreasing on $\left (\frac{5} {2};\infty \right )$.

9000079102

Level:

Find the intervals where the following function is a decreasing function. \[ f(x) = \frac{x^{2} + 1} {x} \]

$[ - 1;0)$ and $(0;1] $

$[ - 1;1] $

$(-\infty ;-1] $ and $[1;\infty) $

$[1;\infty) $

9000079103

Level:

Find the $x$ at which has the function $f$ a local maximum. \[ f(x) = x^{3} - 3x^{2} - 9x + 2 \]

$x=- 1$

$x=- 3$

$x=1$

$x=3$

9000079104

Level:

Find the $x$ at which has the function $f$ a local minimum. \[ f(x) = \frac{\ln x} {x} \]

does not exist

$x = 0$

$x = 1$

$x =\mathrm{e}$

9000079105

Level:

Find all the $x$ at which the function $f$ has local extrema. \[ f(x)= \left (1 - x^{2}\right )^{3} \]

$x=0$

$x_1=0$, $x_2=1$

$x_1=- 1$, $x_2=1$

$x_1=- 1$, $x_2=0$, $x_3=1$

Applications of derivatives

9000070406

9000070407

9000070408

9000070409

9000070410

9000079101

9000079102

9000079103

9000079104

9000079105

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