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1.1 Übungen

Aus Online Mathematik Brückenkurs 2

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Version vom 13:25, 10. Mär. 2009

Theorie

Übungen

Übung 1.1:1

The graph for \displaystyle f(x) is shown in the figure.

a)	What are the signs of \displaystyle f^{\,\prime}(-4) and \displaystyle f^{\,\prime}(1)?
b)	For what values of \displaystyle x is \displaystyle f^{\,\prime}(x)=0?
c)	In which interval(s) is \displaystyle f^{\,\prime}(x) negative?

(Each square in the grid of the figure has width and height 1.)

1.1 - Figure - The graph of f(x) in exercise 1.1:1

Answer

Solution a

Solution b

Solution c

Übung 1.1:2

Determine the derivative \displaystyle f^{\,\prime}(x) when

a)	\displaystyle f(x) = x^2 -3x +1	b)	\displaystyle f(x)=\cos x -\sin x	c)	\displaystyle f(x)= e^x-\ln x
d)	\displaystyle f(x)=\sqrt{x}	e)	\displaystyle f(x) = (x^2-1)^2	f)	\displaystyle f(x)= \cos (x+\pi/3)

Answer

Solution a

Solution b

Solution c

Solution d

Solution e

Solution f

Übung 1.1:3

A small ball, that is released from a height of \displaystyle h=10m above the ground at time \displaystyle t=0, is at a height \displaystyle h(t)=10-\displaystyle\frac{9{,}82}{2}\,t^2 at time \displaystyle t (measured in seconds) What is the speed of the ball when it hits the grounds?

Answer

Answer 1.1:3

Solution

Solution 1.1:3