Assignments

Calculate a maximum, a minimum or a horizontal inflection point of the functions below. We restrict ourselves to local extremes.

1. Determine the extreme of the parabola:

$y=x^2-7x+12$

2. Verify whether the graph of the function has extremes:

$y=x^3+x^2+10x+1$

and if so, whether it is a maximum of a minimum.

3. Determine the extreme of the function:

$y=2x^3-15x^2+36x-2$

and verify whether it is a maximum or a minimum using the sign of the first derivative.

4. Determine the extreme of the function:

$y=2x^3-15x^2+36x-2$

and verify whether it is a maximum or a minimum by using the second derivative.

5. Find the extremes of the function:

$y=\sin(x)$

on the interval interval $[0,2\pi]$ .

6. Find the extremes of the function:

$y=\cos(x)$

on the interval $[0,2\pi]$ . Verify whether they are maxima or minima by using the second derivative.

7. Determine the extremes of the function:

$y=-x^3+9x^2-24x+26$

Verify in which point there is a maximum or a minimum by using the second derivative.

8. Verify whether the function:

$y=\displaystyle\frac{x^2+1}{x}$

has a maximum or a minimum.

9. Verify whether the function:

$y=x\ln(x)$

has a maximum or a minimum.

10. Find the extreme of the function:

$y=2x^3-15x^2+36x-2$

without using the sign of the first derivative or the second derivative.