# derivative

1. ### derivative

Consider the function f(x)=6x-x^2 and the point P(2,f(2)=(2,7)). Find the slopes of secant lines to the graph of y=f(x) determined by P and points on the graph at x=3 and x=1.5
2. ### derivative

Find the the derivative of the function using the chain rule: f(x)=(x^2+4x+6)^5

4. ### Limit of postive function with bounded derivative and convergent improper integral

Is it true that for a continuous function X(t) where X(t)â‰¥0 and \int_{-\infty}^{-T}X(s)ds<\infty and X(t) is bounded together with its derivative: \lim \limits_{tâ†’âˆ’\infty} X(t)=0? If so, why?
5. ### Help with Calculus II Problem

Need help with this one. Can't seem to solve it. Thanks in advance
6. ### Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w))

Hello to my Math Fellows, Problem: I am looking for a way to calculate w-derivative of Fourier transform, d/dw (F{x(t)}), in terms of regular Fourier transform, X(w)=F{x(t)}. Definition Based Solution (not good enough): from I can find that w-derivative of Fourier transform for x(t) is...
7. ### How to find f(x)

It is given that xÂ²(f(x)-f'(x))=e^x for all x>0 and f(1)=e. I have to prove that f(x)=e^x/x. How can I prove that?
8. ### Financial Derivative Pricing

Please could someone help me with this question, Iâ€™d be very grateful :- Suppose that f is a solution of the above Black-Scholes PDE and that f (s,t) = g(s), i.e., Suppose that f may be written as a function of S only. Deduce the general form of f
9. ### Partial derivative

Find \frac{\partial z}{\partial x} for x^{2}+\cos y +z^{3}=1 Please explain what it means.
10. ### Homework Check: Concavity and Second Derivative Test

Please tell me what I need to correct, otherwise thanks for helping to check my Calculus work. Attachment is below, please check to view my answers.

12. ### Concavity and Second Derivative Test Problems Help

Can you help on these sets of problems? I don't understand entirely how to do them, and I have a test coming soon, so I could really use your help. Thanks. Concavity and the Second Derivative Test 2.$\ \ \$Suppose you are given a formula for a function $f$. a)$\ \ \$How do you determine...
13. ### Derivative problems help

Here are some of my practice problems: csc(y^2)=5x+4 and 2x^2+3=e^(2y)^3 Can you show me the steps on each one individually in detail so I can better understand how to do it?
14. ### Second Derivative Test Problem 2

Let f be a twice differentiable function,and let f(1)=-7, f'(1)=0, and f''(1)=-2. What occurs in the graph of f at the point (1,âˆ’7)? I believe the answer is that (1,-7) has a maximum point judging by the second derivative shown above. Am I correct?
15. ### Second Derivative Test Problem

Let h be a twice differentiable function, and let h(-4)=-3, h'(âˆ’4)=0, and h''(-4)=0. What occurs in the graph of h at the point (-4,-3)? So, what should I start doing first?
16. ### On the New Calculus

I would like for my idea on taking a derivative using a new technique evaluated: I have made the post more concise and precise here. All prior messages can be disregarded (particularly the partial definition of a straight line). Some theory (below) before the definitions. This is to convey how...
17. ### n-th derivative

Find n-th derivative of function f(x)=\sin^{n}(x) . n-natural number
18. ### Derivative and continuity

Given the continuous function find a, b and c such that its graph has a tangent touching it at three points.
19. ### Function whose derivative is inversely proportional to the function itself

Is there such a function that its derivative is one divided by the function itself? This would be analogous to how the derivative of an exponantial is directly proportional to the exponential function itself, but in this case Iâ€™m looking for it to be inversely proportional. Does such a...
20. ### Calculate the derivative of a functional.

How to calculate the $J'\left(y\right)$ of $J\left(y\right) = \int_0^1 g\left( y\left( x \right) \right) \operatorname dx$ ? It will be useful if can provide the derivation procss.