- #1
mimi.janson
- 80
- 0
I need to solve questions about f (x) to f ' (x)
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 a lot 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 don't really understand how i can solve it.
i think i might need to use a second quadratic equation but i don't really understand it so if someone could help me with understanding please
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 a lot 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 don't really understand how i can solve it.
i think i might need to use a second quadratic equation but i don't really understand it so if someone could help me with understanding please