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**I need to solve questions about f (x) to f ' (x)**

## Homework Statement

hi i have the function f(x) = -0,8 x^4 + 3,2 x^3 + 0,4 x^2

The function explains the realationsship between time and place while a person is running. (can also be called distance and time). Besides i got told that the person runs for three hours

A) First i get asked to write something that shows the speed as function of time.

So i thought of differentiating it, since that will tell me alot about the slope.

f(x) = -0,8 x^4 + 3,2 x^3 + 0,4 x^2

→

f ' (x)=-32 x^3 + 9,6 x^2 + 0,8 x

B) so my second question was to find out how fast the person runs after 2 hours. Since i know that x is the time and y is the distance i know that i only have to put 2 in the place of x in my function ...i am though not sure if it is in f(x) or f ' (x) but i believe it is in f ' (x) since that was the one telling about the speed.

so i solved it this way

f ' (2)=-32 *2^3 + 9,6 *2^2 + 0,8*2

→

f ' (2)=-256 + 38,4 + 1,6

f '(2) = -216

but there is something wrong here since the speed cannot possibly end up being a negative result ? so i would like someone to show me what i am doing wrong here.

C) last i have a question that asks me to find out where out of the three hours the person runs with the fastest speed .....i dont really understand how i can solve it.

i think i might need to use a second quadratic equation but i dont really understand it so if someone could help me with understanding please