Calculus

The function g(x)=12x^2-sinx is the first derivative of f(x). If f(0)=-2, what is the value of f(2pi)?

a)30pi+2
b)8pi^2-2
c)4pi^3+8
d)32pi^3-2
e)2pi^2+5

1. 👍
2. 👎
3. 👁
1. so f'(x) = 12x^2 - sinx
f(x) = 4x^3 + cosx + c
f(0) = -2
-2 = 0 + cos0 + c
-2 = 1 + c
c = -3
f(x) = 4x^3 + cosx - 3
f(2π) = 32π^3 + 1 - 3
= 32π^3 - 2

1. 👍
2. 👎

Similar Questions

1. calculus

Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation)

2. calculus

A function f is defined on the interval [0,4], and its derivative is e^sinx-2cos3x a. on what interval is f increasing? b. at what value(s) of x does f have a local maxima? c. how many points of inflection does f have? *calculator

3. Calculus. I need help!

Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx. y=√sinx √ is square root.

4. Calculus (Continuity and Differentiability)

Okay. So I am given a graph of a derivative. From what I can gather, it looks like the function might be abs(x-2)-4. (I was not given an explicit function for g', just its graph.) The question then goes on to ask me: Is it

1. Calculus

Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function

2. math

Let f be a real value function and x Î Df then 0 lim ( ) ( ) h f x h f x ® h + - when it exists is called A) The derivative of f at a B) The derivative of f at h C) The derivative of f at x D) The derivative of f at x = h

3. inverse

If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means

Evaluate a/b+c^d for a=6,b=3,c=4 and d=5 A.42*** B.18 C.82 D.360 What is the simplified form of the expression ? -(12x-8y) A.12x+8y B.12x-8y***** C.-12x+8y D.-12x-8y

1. calculus help

Find the derivative of the function. y = integral from cosx to sinx (ln(8+3v)) dv lower limit = cosx upper limit = sinx y'(x) = ????

2. calculus help again

if f'(x)=cos x and g'(x)=1 for all x, and if f(0)=g(0)=0, then the limit x--->0 fo function f(x)/g(x)= okay, so f(x)=sinx g(x)=x and the f(0)=g(0)=0 is also satisfied and equals o. so the limit x-->o of sinx/x= is the answer

3. Math

1) evaluate without a calculator: a)sin(3.14/4) b) cos(-3(3.14)/4) c) tan(4(3.14)/3) d) arccos(- square root of three/2) e) csctheata=2 2) verify the following identities: a) cotxcosx+sinx=cscx b)[(1+sinx)/ cosx] + [cosx/

4. Quantum mechanics, eigenfunctions!

Determine if the function sin(x)*e^(ax) where a=constant is an eigenfunction of the operators d/dx and d^2/(dx)^2 Okay. My understanding is that you use the operator and perform its "thing" on the function. In this case, you will