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1.1 Übungen

Aus Online Mathematik Brückenkurs 2

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|width="100%"| For what values of <math>x</math>-is <math>f^{\,\prime}(x)=0</math>?
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|width="100%"| For what values of <math>x</math> is <math>f^{\,\prime}(x)=0</math>?
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| valign="top" |c)
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|width="100%"| In which interval(s) is<math>f^{\,\prime}(x)</math> negative?
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|width="100%"| In which interval(s) is <math>f^{\,\prime}(x)</math> negative?
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(Each square in the grid of the figure has width and height 1.)
(Each square in the grid of the figure has width and height 1.)

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exercise 1.1:1

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

a) What are the signs of f(5) and f(1)?
b) For what values of x is f(x)=0?
c) In which interval(s) is f(x) negative?

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

1.1 - Figur - Grafen till f(x) i övning 1.1:1

exercise 1.1:2

Determine the derivative f(x) when

a) f(x)=x23x+1 b) f(x)=cosxsinx c) f(x)=exlnx
d) f(x)=x  e) f(x)=(x21)2 f) f(x)=cos(x+3)

exercise 1.1:3

A small ball, that is released from a height of h=10m above the ground at time t=0, is at a height h(t)=102982t2 at time \displaystyle t (measured in seconds) What is the speed of the ball when it hits the grounds?

exercise 1.1:4

Determine the equation for the tangent and normal to the curve \displaystyle y=x^2 at the point \displaystyle (1,1).

exercise 1.1:5

Determine all the points on the curve \displaystyle y=-x^2 which have a tangent that goes through the point \displaystyle (1,1).