Mar 18, 2017 · How do you use the quotient rule to find the derivative of #y=tan(x)# ?

Jan 5, 2017 · What does #f(x)=y# mean? How do you write the total cost of oranges in function notation, if each orange cost $3? How do you rewrite #s=2t+6# in function notation?

Dec 8, 2011 · Assume that f is a differentiable function such that f(0)=f'(0)=0 and f''(0)>0. Argue that there exists a positive constant a>0 such that f(x)>0 for all x in the interval (0,a). Can anything be concluded about f(x) for negative x's? Homework Equations The Attempt at a Solution I think I should use the MVT so here is what I tried:

The derivative of a function f(x) is written f'(x) and describes the rate of change of f(x). It is equal to slope of the line connecting (x,f(x)) and (x+h,f(x+h)) as h approaches 0. Evaluating f'(x) at x_0 gives the slope of the line tangent to f(x) at x_0.

Nov 28, 2017 · The value of F'(0) is 96. Consider: y = f(g(x)) Then by the chain rule the derivative is given by f'(g(x)) * g'(x). Thus the derivative of y = f(g(h(x)) will be ...

To evaluate the constant introduced through integration, it is necessary to know something about the function. Given the value of the integrated function at a point x, plugging in that value gives the constant.

Feb 3, 2009 · If f(x_0)=c and c > 0 then the function must go up to atleast c, and since it is continuous it does not "jump" there. I was thinking of making a small partition of a,x_0, and b. I then know what the sup or inf values of the two rectangles (speaking of the hieghts) will be greater than or equal to x_0 for the upper sum.

SOLUTION: Given f(x) = x2 + 3x – 5, find f(0). -5 Did I do this right. Can you show me the steps

Dec 4, 2016 · 6. (f @ g)(x) can be written as f(g(x)). The chain rule for derivatives deals with composite functions. It states that for f(g(x)), dy/dx = f'(g(x))g'(x) We now insert our given values inside the derivative formula f'(g(0))g'(0) = f'(0)(3) = 2(3) = 6 Hopefully this helps!

Apr 22, 2017 · Integrate twice and then use the boundary conditions to solve for the constants. Given: f''(x) = 4 + cos(x), f(0)=-1, and f((7pi)/2)=0 Integrate: f'(x) = intf''(x)dx = int4 + cos(x)dx f'(x) = 4x + sin(x) + C_1 Integrate again: f(x) = intf'(x)dx = int4x + sin(x) + C_1dx f(x) = 2x^2 - cos(x) + C_1x + C_2 Use the first boundary condition to find the value of C_2 f(0) = -1 = 2(0)^2 - cos(0) …