Petrus
- 702
- 0
Hello MHB,
Sorry for the bad title as I did not know what to name this but this is a problem from my calculus exam which I have not decide if I shall travel 2h to get my exam and see if I got some less point then I should.. (I just got the facit for the exam and I think that I am between one higher grade that I should get)
"Supposed that $$f(x)$$ is a function so that a tangent to function graf is $$x=2$$ goes through $$(0,1)$$. Supposed that also $$f(2)=5$$ and $$g(x)=\frac{f(x)}{x}$$
(a) show that $$g'(2)=-\frac{1}{4}$$
What I did:
$$g'(x)=\frac{f'(x)x-f(x)}{x^2}$$
We know that $$g'(2)=-\frac{1}{4}$$ and $$f(2)=5$$ so I did do like this
$$-\frac{1}{4}=\frac{2f'(x)-5}{2^2}$$ that means $$f'(2)=2$$ and that means this is true only if $$f'(2)=2$$
Facit say:
they first start to calculate the tangent to the graph of $$f$$ for $$x=2 $$ gives of $$f'(2)=\frac{y-f(2)}{x-2}$$
we know that $$f(2)=5$$ also that the point $$(x,y)=(0,1)$$ and if we put those value on the above we get that $$f'(2)=2$$ and then they did same as me but what so you think about how I did it?
Regards,
$$|\pi\rangle$$
Sorry for the bad title as I did not know what to name this but this is a problem from my calculus exam which I have not decide if I shall travel 2h to get my exam and see if I got some less point then I should.. (I just got the facit for the exam and I think that I am between one higher grade that I should get)
"Supposed that $$f(x)$$ is a function so that a tangent to function graf is $$x=2$$ goes through $$(0,1)$$. Supposed that also $$f(2)=5$$ and $$g(x)=\frac{f(x)}{x}$$
(a) show that $$g'(2)=-\frac{1}{4}$$
What I did:
$$g'(x)=\frac{f'(x)x-f(x)}{x^2}$$
We know that $$g'(2)=-\frac{1}{4}$$ and $$f(2)=5$$ so I did do like this
$$-\frac{1}{4}=\frac{2f'(x)-5}{2^2}$$ that means $$f'(2)=2$$ and that means this is true only if $$f'(2)=2$$
Facit say:
they first start to calculate the tangent to the graph of $$f$$ for $$x=2 $$ gives of $$f'(2)=\frac{y-f(2)}{x-2}$$
we know that $$f(2)=5$$ also that the point $$(x,y)=(0,1)$$ and if we put those value on the above we get that $$f'(2)=2$$ and then they did same as me but what so you think about how I did it?
Regards,
$$|\pi\rangle$$